Calculus 1 Final Exam Review Problems and Solutions

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#calculus #calculus1 #apcalculus

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(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

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