Calculus 1 Final Exam Review Problems and Solutions

Ace your Calculus 1 Final Exam! https://www.youtube.com/watch?v=2AG_Dt3x7q0. I work through many Calculus 1 final exam practice problems and their solutions. Problem types: Fundamental Theorem of Calculus, Mean Value Theorem, L’Hopital’s Rule, Optimization, Related Rates, Implicit Differentiation, and more. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

🔴 Ultimate AP Calculus AB Review: https://www.youtube.com/playlist?list=PLmU0FIlJY-Ml4Ha5USN0kSt4TyvamTJar

🔴 AP Calculus AB Exam Review: Practice Exam Problems & Solutions (Multiple Choice, No Calculator): https://www.youtube.com/watch?v=2AG_Dt3x7q0

🔴 AP Calculus AB Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=RLgUwP44V_M

🔴 AP Calculus BC Exam Review: Practice Exam (30 Question Multiple Choice, No Calculator): https://www.youtube.com/watch?v=1Q7ALcwT97A

🔴 AP Calculus BC Exam Review: Free Response Practice Exam Problems & Solutions: https://www.youtube.com/watch?v=ZWisJEDP44w

🔴 Calculus 1 Exam 1 Review Problems and Solutions (Precalculus, Limits, Continuity, Derivatives): https://www.youtube.com/watch?v=UjmvUwvd7c4

🔴 Calculus 1 Course, Lecture 1: The Big Ideas (Rates & Areas, the Infinity Principle & Circular Area): https://www.youtube.com/watch?v=2V_ehJC5QUY

🔴 Calculus 1 Course Lecture Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-MkFrKtM0S0NLu-TxZa5jBIx

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=lmCjnxzIals

🔴 Calculus 1, Lesson 1.2: Exponential Functions: https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus 1, Lesson 1.3: Quadratic Functions, Transformations of Functions, and Function Composition: https://www.youtube.com/watch?v=1T58CnSME4g

🔴 Calculus 1, Lesson 1.4: Logarithmic Functions (Intro to Horizontal Compressions & Inverse Functions): https://www.youtube.com/watch?v=oS-gvIoJf60

🔴 Calculus 1, Lesson 1.5: Trigonometric Functions and Inverse Trigonometric Functions: https://www.youtube.com/watch?v=UFYjlnGUenE

#calculus #calculus1 #apcalculus

Links and resources
===============================
🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1
🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/
🔴 Follow me on Twitter: https://twitter.com/billkinneymath
🔴 Follow me on Instagram: https://www.instagram.com/billkinneymath/
🔴 You can support me by buying “Infinite Powers, How Calculus Reveals the Secrets of the Universe”, by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA.
🔴 Check out my artist son Tyler Kinney’s website: https://www.tylertkinney.co/

(0:00) True/False questions about theorems (Increasing Function Theorem, Extreme Value Theorem, Mean Value Theorem)
(9:56) Units for a definite integral
(12:09) Rate of change and linear approximation
(16:29) Definite integral properties to evaluate the integral of a linear combination of functions
(19:01) Find a derivative (Quotient Rule, Product Rule, Chain Rule, memorized derivatives)
(23:09) Evaluate a definite integral with the Fundamental Theorem of Calculus
(26:27) Differentiate an integral (variable in the upper limit of integration). Need the Fundamental Theorem of Calculus.
(28:50) L’Hopital’s Rule limit calculation (0/0 indeterminate form)
(31:57) Definite integral as a limit of a Riemann sum (right-hand sum)
(33:16) Temperature and average temperature (average value of a function)
(38:21) Numerical integration of data (upper estimate and lower estimate)
(43:26) Free fall (find the maximum height)
(48:26) Related rates (sliding ladder)
(52:37) Implicit differentiation
(58:03) Global optimization. Relate to bounds for a definite integral.
(1:04:39) Construct an antiderivative graphically (use Fundamental Theorem of Calculus)
(1:10:46) Solve a differential equation initial value problem (pure antiderivative problem)
(1:11:57) Graphically interpret symbolic quantities as lengths, slopes, and areas.
(1:15:38) Average value of a function
(1:18:11) Limit definition of the derivative (calculate a derivative as a limit of slopes of secant lines)
(1:21:28) Minimize surface area of circular cylinder (fixed volume)
(1:26:32) Extreme Value Theorem necessary hypothesis
(1:28:39) Mean Value Theorem necessary hypothesis
(1:29:51) Constant Function Theorem corollary proof
(1:32:51) Racetrack Principle corollary proof

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.