Calculus 1 Exam 1 Review Problems and Solutions: Precalculus, Limits, Continuity, Derivatives

Types of problems: 1) Precalculus functions (linear, power, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric), 2) applications, 2) limits, 3) continuity, 4) limit definition of the derivative. Infinite Powers: https://amzn.to/37PBMjb.

Also included are: vertical asymptotes, horizontal asymptotes, slant asymptotes, limits at infinity, algebraic properties of limits, logarithm proof, free fall, depreciation, and Poiseuille’s Law.

🔴 Calculus 1, Lesson 1.1: Linear Functions (3Blue1Brown SoME2): https://www.youtube.com/watch?v=47ZqW19AjD4

🔴 Calculus Homework Help Playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-Mnwt_N6fFINl7IwB6FkZTBC

🔴 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

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(0:00) Types of problems to expect
(0:18) Which function dominates as x goes to infinity?
(0:52) Find log base 3 of 81
(1:23) Find log base 2 of 1/16
(1:54) Is f(x) = |x|/x continuous for all x?
(2:09) What if f(0) is defined to be 0 (make f a piecewise function)?
(4:00) Find a horizontal asymptote of a rational function
(6:11) Use polynomial long division to find a slant asymptote
(9:31) Find an exact value of sine using the Pythagorean identity and the unit circle definition
(13:50) Find an inverse function
(15:57) Solve a trigonometric equation using an inverse trigonometric function.
(20:55) Find a polynomial formula for a given graph with given intercepts
(23:38) Free fall: when does it hit the ground? Also find an average velocity over a time interval. Sketch a graph of the quadratic function showing a secant line with appropriate slope.
(29:27) Find the distance to travel so the cost of two car rentals is the same (use linear functions).
(32:22) Poiseuille’s Law (gas flow) power function proportionality problem.
(36:02) Find a sinusoidal function with a given graph (given vertical shift, amplitude, period, and horizontal shift).
(40:39) Algebraic limit properties problem to confirm a horizontal asymptote
(43:25) Rational function with a removable discontinuity. Find asymptotes and a limit.
(47:28) Limit definition of the derivative problem (show steps and give brief reasons).
(51:40) Logarithm property proof.
(55:44) Depreciation problem (exponential decay, including finding a continuous relative rate of decay).

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