Ap calculus bc practice mcq
Practice Exam. The questions contained in this AP® Calculus BC Practice Exam are written to the content specifications. of AP Exams for this subject. Taking this practice …
Do we owe the emergence of language and self-reflection to the ancient and sustained consumption of psilocybin mushrooms? Advertisement Psychedelic research has experienced a renai...Visit the College Board on the Web: www.collegeboard.org. Scoring Worksheet The following provides a scoring worksheet and conversion table used for calculating a composite score of the exam. 201 AP Calculus BC — AB Subscore Scoring Worksheet Section I: Multiple Choice Questions (1-4, 7, 11, 14, 18, 22-27, 76-78, 80-82, 84-85, 87-88, 90-92) 1 ...2003 BC Multiple Choice Answers and Solutions. Return to Mr. Calculus.2006 AP Calculus Practice Exams (Keys Are Provided For The Multiple Choice Portions) This site is sponsored by the Department of Mathematics at the University of Houston.Please report any errors to Jennifer Marsala at [email protected].. Check out the current practice materials, and register to access the online practice exams and … The questions contained in this AP Calculus BC Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus BC Practice Exam has never been administered as an operational AP Exam, statistical ... May 5, 2021 ... Comments3 ; Practice AP Calculus Exam Questions - FRQ with Calculator! · 165 views ; AP Calculus AB 2012 Multiple Choice (calculator) - Questions ...
AP® Calculus BC Exam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions Section I of this examination contains 45 multiple-choice questions. Fill in only the ovals for numbers 1 through 45 on your answer sheet. CALCULATORS MAY NOT BE USED IN THIS PART OF THE …A. 0.340. What is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=√100−4x^2 and the x- and y-axes is revolved about the y-axis? B. 523.599. Let R be the region in the first quadrant bounded by the graph of y=2tan (x/5), the line y=5−x, and the y-axis.This course is organized around the following big ideas: Big Idea 1: Limits. Big Idea 2: Derivatives. Big Idea 3: Integrals and the Fundamental Theorem of Calculus. Big Idea 4: Series. The AP Calculus BC exam format is: Section I: Multiple Choice. Part A (60 minutes, calculator not permitted) 30 Questions.About the Exam. The AP Calculus BC Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations. A graphing calculator is permitted for parts of the exam. In this video, we’ll unpack sample multiple-choice questions.Download questions here: https://tinyurl.com/24yuem6uStay motivated and keep preparing for AP Ex...
2008 AP Calculus Multiple Choice Solutions: Home AB Non-Calculator Section: AB ... BC #86 AB/BC #87 BC #88 AB/BC #89 BC #90 BC #91 BC #92 Powered by Create your own unique website with customizable templates. Get Started ...360 | 550 AP Calculus AB & BC Practice Questions Section I CALCULUS AB SECTION I, Part B Time—50 Minutes Number of questions—17 A GRAPHING CALCULATOR IS REQUIRED FOR SOME QUESTIONS ON THIS PART OF THE EXAMINATION Directions: Solve each of the following problems, using the available space for scratchwork. After examining the form of theSep 2, 2023 ... Comments7 · AP Calculus BC Practice Exam 2012 - Calculator Multiple Choice questions 76-92 · March 2024 Digital SAT, 4 Score Reactions (we got .....AP Calculus BC Multiple Choice 2016 Questions - Practice Exam (pdf) Part A, Q1 - 14. Part A, Q15 - 28. Show Video for Q15 - 28. Part B, Q76 - 92. Show Video for Q76 - 92. Limits. For time > 0, the position of a particle moving in the xy-plane is given by the vector. Consider the series.AP Calculus BC Scores. AP scores are reported from 1 to 5. Colleges are generally looking for a 4 or 5 on the AP Calculus BC exam, but some may grant credit for a 3. Learn more about college AP credit policies. Each test is curved so scores vary from year to year. Here’s how AP Calculus BC students scored on the May 2020 test: Score.
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In this AP Daily: Live Review session for AP Calculus BC, we will focus on preparing for integration questions on the AP Calculus BC Exam. AP-style free-resp... In this video, we’ll unpack sample multiple-choice questions.Download questions here: https://tinyurl.com/53xrdbacStay motivated and keep preparing for AP Ex... AP Calculus BC Multiple Choice 2012 Question 1. If y = sin 3 x, then dy/dx =. (A) cos 3 x (B) 3cos 2 x (C) 3sin 2 x (D) -3sin 2 xcos x (E) 3sin 2 x cos x. Show Video Lesson. AP Calculus BC Multiple Choice 2012 Question 2. 2. The position of a particle moving in the xy-plane is given by the parametric equations x (t) = t 3 2 and y (t) = 12t - 3t 2. 5. State the component form and length of the vector ν with initial point A (2, -1) and terminal point B (-1, 3) . 6. Given compute the derivative vector. 7. The graphs of the polar curves r = 2 + cos θ and r = -3 cos θ are shown on the graph below. The curves intersect when and . Region R is in the second quadrant, bordered by each curve ... 1. Crack AP. Crack AP is an online education platform that provides students with a variety of practice tests for different exams like AP, SAT, and ACT, for free. It provides practice test questions for all AP exams including AP Calculus BC. The practice test comprises both MCQs and FRQs.Practice Test 1. AP® Calculus BC Exam. SECTION I: Multiple-Choice Questions. The Exam. DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. At a …
The AP Calculus AB Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted).CALCULUS BC SECTION II, Part A. Time—30 minutes Number of problems—2. A graphing calculator is required for these problems. 1. On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant. is modeled by G t …AP Calculus BC solved exams. Unit 12. AP®︎ Calculus BC Standards mappings. Course challenge. Test your knowledge of the skills in this course. Start Course challenge. ... Practice. Verify solutions to differential equations Get 3 of 4 questions to level up! Sketching slope fields. Learn. Slope fields introductionMultiple Choice - A Calculator May Be Used On This Section: 13. Let f(x) = x3 7x2+25x 39 and let gbe the inverse function of f. What is the value of g0(0)? (A) 1 25 (B) 1 25 (C) 1 10 (D) 10 (E) 25 f(x) = ˆ e x +2 for x<0 ax+b for x 0 14. Let f be the function de ned above, where aand bare constants. If f is di erentiable at x= 0, what is the ...Complete Practice Tests. The College Board has released two complete exams from prior administrations of the AP Calculus AB exam. The tests are from 1988 and 1998. The 1988 test has an answer key included; however, for some reason, the 1998 exam does not. The College Board provided answers for the free-response questions in a separate document ...AP Calculus (BC) Chapter 6 Test No Calculator Section Name: Date: Period: Part I. Multiple-Choice Questions (5 points each; please circle the correct answer.) 1. Zp ... Multiple-Choice Questions (5 points each; please circle the correct answer.) 8. You are given the differential equation dy dx = 1 5 p y, where y(0) = 25. For whichWe can analyze the average AP® Calculus BC score more efficiently by considering a multi-year trend. We can refer to the AP® Student Score Distributions, released by the College Board annually. These reports show us that the mean score was 3.81 in 2014, 3.72 in 2015, 3.80 in 2016, 3.78 in 2017, 3.74 in 2018, 3.80 in 2019 and …Mar 20, 2024 ... In this video I go over Multiple Choice Questions (MCQ) 1-12 from the 1998 AP Calculus AB Exam.What is the sum of the series 1. (E) The series diverges. 21. A particle moves along a straight line. The graph of the particle’s position x ( t ) at time t is shown above for 0 < t < 6. The graph has horizontal tangents at t = 1 and t = 5 and a point of inflection at t = 2.
AP Calculus BC Practice Exam From the 2 016 Administration This exam ma y no t be posted on school or persona l websites , no r electronically redistribute d fo r an y reason . Thi s Released Exa m is provided by th e Colleg e Boar d for AP Exam preparation . Teacher s ar e permitted to download th e material s an d mak e copies to use wit h thei r student s in a classroo m settin g onl y. To ...
AP Calculus BC – Parametric Equations AP Test Practice FRQ.1 (calculator) FRQ.2 (calculator) FRQ.3 (calculator) MC.1 MC.2 MC.3 MC.4. MC.5 MC.6 MC.7 MC.9 (calculator) MC.10 (calculator) At time t O, a particle moving along a curve in the xy-plane has position (x(t), y(t)) with velocity vectorWhen you set up your wireless connection, the router or device that enables the connection is called an access point. The AP name is the name by which other devices list your wirel...Apr 14, 2022 ... ... practice for the AP Calculus BC exam. These would also be extremely useful to anyone in a Calc II class. I tried to focus on questions about ... AP Calculus AB and BC Course and Exam Description About AP College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses AP Calculus BC Scoring Guidelines from the 2019 Exam Administration Author: College Board ... 2019 AP exam administration; teacher resources; exam resources; exam practice; exam scoring information; exam preparation; course preparation; AP Scoring Guidelines from the 2019 Exam Administration; £½? 7÷ø¶Â ´ O ÿuÞ¨Ó Øau^K9 éÚ` ...AP Calculus (BC) Chapter 6 Test No Calculator Section Name: Date: Period: Part I. Multiple-Choice Questions (5 points each; please circle the correct answer.) 1. Zp ... Multiple-Choice Questions (5 points each; please circle the correct answer.) 8. You are given the differential equation dy dx = 1 5 p y, where y(0) = 25. For whichApproaches 0 and is decreasing so it is convergent. Comparison Test. Let 0 ≤ an ≤ bn, for all n. 1) If ∑bn converges, then ∑an converges. 2) If ∑an diverges, then ∑bn diverges. Limit Comparison Test. if the limit as n approaches infinity of (given series/chosen series) is >0, the two series will converge/diverge together. Integral ...Part A: 2 questions, 30 minutes, 18.75% of exam score (graphing calculator required) Question 1: Focus on function concepts. Question 2: Modeling a non-periodic …
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36. 2012 The College Board. Visit the College Board on the Web: www.collegeboard.org. AP Exam Instructions. the calculator to remove exam questions and/or answers from the room may result in the cancellation of AP Exam scores. The AP Calculus AB Exam and the AP Calculus BC Exam should be administered simultaneously. Section I: Multiple-Choice Questions. This is the multiple-choice section of the 2016 AP exam. It includes cover material and other administrative instructions to help familiarize students with the mechanics of the exam. (Note that future exams may differ in look from the following content.) AP ® Calculus AB Exam. SECTION I: Multiple Choice 2016 AP®Calculus BC Exam. SECTION I: Multiple-Choice Questions. DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions. Section I of this examination contains 45 multiple-choice questions. Fill in only the ovals for numbers 1 through 45 on your answer sheet. CALCULATORS MAY NOT BE USED IN THIS PART OF THE EXAMINATION.Return to Mr Calculus. 2012 Practice Test AP Multiple Choice AB answers and solutions (BC below) Part A no calculator allowed Problems 1-9 Problems 10-16 Problems 17-24 …The AP Calculus BC Exam will have both paper and digital formats in 2021. The paper administration is held on May 4, 2021 and May 24, 2021: Section I: Multiple Choice, 50% of exam score. No calculator: 30 questions (60 minutes) Calculator: 15 questions (45 minutes) Section II: Free Response, 50% of exam score.Eloise Theisen is an adult geriatric nurse practitioner with more than two decades of experience in nursing, including 14 years of oncology at John Muir Health in Walnut Creek, Cal...Visit the College Board on the Web: www.collegeboard.org. Scoring Worksheet The following provides a scoring worksheet and conversion table used for calculating a composite score of the exam. 201 AP Calculus BC — AB Subscore Scoring Worksheet Section I: Multiple Choice Questions (1-4, 7, 11, 14, 18, 22-27, 76-78, 80-82, 84-85, 87-88, 90-92) 1 ...Only on the BC Test. 17-18% of the test. Roughly 7 to 8 multiple choice questions. Always one FRQ on this unit (usually FRQ 6) Developing Understanding . Well, after going through countless limits, derivatives, and integrals, you’ve made it here! Welcome to Unit 10, the last unit of AP Calculus BC!AP Calculus Practice Exams. This site is sponsored by the Department of Mathematics at the University of Houston. Please report any errors to Jennifer Marsala at [email protected]. Check out the current practice materials, and register to access the online practice exams and practice quizzes by topic that are automatically graded. ….
AP Calculus BC 2020 Sample Free Response Question 1. A function f has derivatives of all orders for all real numbers x. A portion of the graph of f is shown above, along with the line tangent to the graph of f at x = 6. Selected derivatives of f are given in the table above. AP Calculus BC 2020 Sample Free Response Question 2. 2. The questions contained in this AP Calculus BC Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus BC Practice Exam has never been administered as an operational AP Exam, statistical ... Write your responses to this question only on the designated pages in the separate Free Response booklet. Write your solution to each part in the space provided for that part. 2. A particle moving along a curve in the xy-plane is at position ( x ( t ) , y ( t ) ) at time t 0 . The particle moves in.The calculus can change dramatically if you have other assets like a pension. By clicking "TRY IT", I agree to receive newsletters and promotions from Money and its partners. I agr...In this AP Daily: Live Review session for AP Calculus BC, we will focus on preparing for integration questions on the AP Calculus BC Exam. AP-style free-resp...Jan 15, 2024 ... In this video I go over a Parallel Version of Multiple Choice Questions from the 2020 AP Calculus AB Practice Exam MCQ #6-10.AP® Calculus Multiple-Choice Question Collection 1969–1998 ... For more information about equity and access in principle and practice, please send an email ... 1973 AP Calculus BC Exam, Section 1 29 1985 AP Calculus AB Exam, Section 1 38 1985 AP Calculus BC Exam, Section 1 47AP® Calculus BC Exam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions Section I of this examination … 6 AP CALCULUS BC PRACTICE EXAM AP CALCULUS BC PRACTICE EXAM 7 11. liIf m x dx k p k 1 "3 # is finite, then which of the following must be true? I. x 1 p n 1 3-= / converges II. x 1 p n 1 3 = / diverges III. x 1 p n 1 2 3 = / converges A. I only B. II only C. III only D. I and III E. II and III 12. x tIn the xy-plane, the graph of the parametric ... The AP Calculus AB exam has two sections: Section I contains 45 multiple-choice questions for which you are given 105 minutes to complete. Section II contains 6 free-response questions for which you are given 90 minutes to complete. The total time allotted for both sections is 3 hours and 15 minutes. Ap calculus bc practice mcq, AP Calculus BC is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of ... , Course: AP®︎/College Calculus BC > Unit 6. Lesson 13: Using integration by parts. Integration by parts intro. Integration by parts: ∫x⋅cos (x)dx. Integration by parts: ∫ln (x)dx. Integration by parts: ∫x²⋅𝑒ˣdx. Integration by parts: ∫𝑒ˣ⋅cos (x)dx. Integration by parts. Integration by parts: definite integrals., D) dT/dt = k (T - 75) dT/dt is found same way as the last question. "dT/dt is proportional to the difference between the egg's temperature in degrees Fahrenheit (F) and the room temperature of 75F" The egg's temperature is T, and the room temperature is 75. The difference means T - 75. "y is proportional to x., AP Calculus BC Multiple Choice 2003 Questions - Practice Exam (pdf) Part A, Q1 - 28. Part B, Q76 - 92. For 0 ≤ t ≤ 13 an object travels along an elliptical path given by the parametric equations x = 3cos t and y = 4sin t. At the point where t =13, the object leaves the path and travels along the line tangent to the path at that point., The AP Calculus BC framework is organized into 10 commonly taught units of study that provide one possible sequence for the course. ... that students should practice throughout the year—skills that will help them learn to think and act like mathematicians. Skill. Description. Exam Weighting (Multiple-Choice Section) Exam Weighting (Free ..., AP Calculus BC – Parametric Equations AP Test Practice FRQ.1 (calculator) FRQ.2 (calculator) FRQ.3 (calculator) MC.1 MC.2 MC.3 MC.4. MC.5 MC.6 MC.7 MC.9 (calculator) MC.10 (calculator) At time t O, a particle moving along a curve in the xy-plane has position (x(t), y(t)) with velocity vector, 2012 Practice Test AP Multiple Choice BC answers and solutions Part A no calculator allowed Problems 1-8 Problems 9-14 Problems 15-22 Problems 23-28 Part B calculator allowed Problems 76-85. Problems 86-92. Return to Mr Calculus ..., Study with Quizlet and memorize flashcards containing terms like What is a limit?, Write: the limit as x approaches a of the function of x is equal to L, lim (x→-2) (x³+8)/(x+2)=? and more., 2. The volume of the solid that results when the area between the curve y = ex and the line y = 0, from x = 1 to x = 2, is revolved around the x -axis is. 3. dx =. 4. If y = 5 x2 + 4 x and x = ln t, then =. 5. If f ( x) =. 6. The tangent line to the curve y = x3 - 4 x + 8 at the point (2, 8) has an x -intercept at. , the multiple-choice questions in this exam. for the free-response questions in this exam. increasing at a rate of 1.35 cubic feet per minute per minute. ∫0 g ( t ) dt cubic feet. 61.749 (or 61.748) cubic feet. time t = 6. © 2018 The College Board. The position of the particle at time t = 2 is (1.461, 4.268 ) ., Write your responses to this question only on the designated pages in the separate Free Response booklet. Write your solution to each part in the space provided for that part. 2. A particle moving along a curve in the xy-plane is at position ( x ( t ) , y ( t ) ) at time t 0 . The particle moves in., y = cx 4 x 2 , for some c. Each spinning toy is in the shape of the solid generated when such a region is. −. revolved about the x-axis. Both x and y are measured in inches. (a) Find the area of the region in the first quadrant bounded by the x-axis and the graph of y = cx 4 x2 − for c = 6. dy c 2x (4., The AP Calculus BC exam consists of 45 multiple-choice questions and six free-response questions. The multiple choice and free-response sections each represent 50% of your score. The total exam duration is 3 hours and 15 minutes., 2003 BC Multiple Choice Answers and Solutions. Return to Mr. Calculus., Write your responses to this question only on the designated pages in the separate Free Response booklet. Write your solution to each part in the space provided for that part. 2. A particle moving along a curve in the xy-plane is at position ( x ( t ) , y ( t ) ) at time t 0 . The particle moves in., AP Calculus BC 2021 Free Response Question 1. The density of a bacteria population in a circular petri dish at a distance r centimeters from the center of the dish is given by an increasing, differentiable function f, where f (r)is measured in milligrams per square centimeter. Values of f (r) for selected values of r are given in the table ..., AP Calculus Practice Exams. This site is sponsored by the Department of Mathematics at the University of Houston. Please report any errors to Jennifer Marsala at [email protected]. Check out the current practice materials, and register to access the online practice exams and practice quizzes by topic that are automatically graded., The questions contained in this AP Calculus BC Practice Exam are written to the content specifications of AP Exams for this subject. Taking this practice exam should provide students with an idea of their general areas of strengths and weaknesses in preparing for the actual AP Exam. Because this AP Calculus BC Practice Exam has never been administered as an operational AP Exam, statistical ... , Students who successfully complete AP Calculus BC courses are invited to take the AP Calculus BC exam to demonstrate what they have learned and potentially earn college credit. The AP Calculus exam lasts for three hours and fifteen minutes and consists of a 45-question, 105-minute multiple-choice section and a six-question, 90-minute free ... , AP Calculus AB and BC Course and Exam Description About AP College Board’s Advanced Placement® Program (AP®) enables willing and academically prepared students to pursue college-level studies—with the opportunity to earn college credit, advanced placement, or both—while still in high school. Through AP courses, A Walt Disney World annual pass is the cheapest way to visit Disney World theme parks multiple times a year plus discounts! Save money, experience more. Check out our destination h..., AP Calculus BC Multiple Choice 2016 Questions - Practice Exam (pdf) Part A, Q1 - 14. Part A, Q15 - 28. Show Video for Q15 - 28. Part B, Q76 - 92. Show Video for Q76 - 92. Limits. For time > 0, the position of a particle moving in the xy-plane is given by the vector. Consider the series., AP® Calculus BC Exam SECTION I: Multiple-Choice Questions DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO. Instructions Section I of this examination contains 45 multiple-choice questions. Fill in only the ovals for numbers 1 through 45 on your answer sheet. CALCULATORS MAY NOT BE USED IN THIS PART OF THE …, Complete Practice Tests. The College Board has released two complete exams from prior administrations of the AP Calculus AB exam. The tests are from 1988 and 1998. The 1988 test has an answer key included; however, for some reason, the 1998 exam does not. The College Board provided answers for the free-response questions in a separate document ... , Visit the College Board on the Web: www.collegeboard.org. AP Central is the oficial online home for the AP Program: apcentral.collegeboard.org. 1. 300 (a) ∫ r ( t ) dt = 270. 0. According to the model, 270 people enter the line for the escalator during the time interval 0 ≤ t ≤ 300. (b) 20 + ∫ ( 300 ( 300., 2023 AP Daily: Practice Sessions AP Calculus BC Session 1 – MCQ 1. Which of the following is a logistic differential equation whose solution has carrying capacity of 50? A. 𝑑 =50 𝑑𝑡 B. 𝑑 = (1− ) 𝑑𝑡 50 C. 𝑑 =50 (1− ) 𝑑𝑡 D. 𝑑 = (1− ) 𝑑𝑡 50 2., Section I: Multiple-Choice Questions. This is the multiple-choice section of the 2016 AP exam. It includes cover material and other administrative instructions to help familiarize students with the mechanics of the exam. (Note that future exams may differ in look from the following content.) AP ® Calculus AB Exam. SECTION I: Multiple Choice 2016, AP Calculus BC Multiple Choice 2016 Questions - Practice Exam (pdf) Part A, Q1 - 14. Part A, Q15 - 28. Show Video for Q15 - 28. Part B, Q76 - 92. Show Video for Q76 - 92. Limits. For time > 0, the position of a particle moving in the xy-plane is given by the vector. Consider the series., The calculus can change dramatically if you have other assets like a pension. By clicking "TRY IT", I agree to receive newsletters and promotions from Money and its partners. I agr..., Kranish AP Calculus. Home Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Calculus AB Final Exam Review Unit 8 Unit 9 Unit 10 Unit 11 AP Calculus BC Final Exam Review Project Unit 10 -Sequences & Series (Part 2) *Quiz (Days 1 - 5): Thursday, March 8th *Unit 10 Test: Thursday, March 15th ... Free Response Practice (March 12th & 13th) Notes ..., AP Calculus BC 2014 Free Response Questions - Complete Paper (pdf) AP Calculus BC 2014 Free Response Question 1. A graphing calculator is required for these problems. 1. Grass clippings are placed in a bin, …, Practice. Free Response. Assessments. Overview. Looking for an AP® Calculus score calculator? Click here for this and more tips for your test! Standards. Tags. Review Albert's AP® Calculus math concepts, from limits to infinity, with exam prep practice questions on the applications of rates of change and the accumulation of small quantities., About this unit. Limits describe the behavior of a function as we approach a certain input value, regardless of the function's actual value there. Continuity requires that the behavior of a function around a point matches the function's value at that point. These simple yet powerful ideas play a major role in all of calculus.