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Calculating limits exactly Use the definition of the derivative to evaluate the following limits.
103.
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Calculus: Early Transcendentals, 2nd Edition
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- Assignment 1: Derive the Product Rule formula using the definition of a derivative. Your derivation should be neat and clear so that any Calculus student can follow. After EVERY STEP, write one sentence explaining your logic. The following are a few definitions and tips: (1) Definition of the derivative: lim h→0 f (x+h)-f(x) h (2) Use a "magic trick": -f(x + h)g(x) + f(x + h)g(x) (this expression is = 0, so essentially we did not change anything) (3) Factor out f (x + h) and g(x): -f(x + h)g(x) + f(x + h)g(x) To start you off, using the definition of a derivative: f(x + h)g(x + h) lim h→0 -f(x)g(x) harrow_forwardPls help ASAP. Pls do this question with all the steps and explanations pls pls pls dont miss any steps.arrow_forwardUsC the definition of denivative f(x) = 6x² - 3x 2. f(1+h)-f(1) lim harrow_forward
- Determining limits analytically Determine the following limits. a. lim tS-2 2 - 5t + 6t A - 412 b. lim tS-2- t - 5 + 6t A - 42 2 - 52 + 6t c. lim tS-2 P - 5 + 6t * - 4r d. lim A - 4 2arrow_forwardTopic : Limits of algebraic functionsarrow_forwardand radical) What I Know Multiple Choice. Directions: Encircle the letter of the correct answer. 1. Which mathematical expression corresponds to the statement "the limits of the function x2 + 2 as x approaches to 3 is equal to 11"? C. lim (x2 + 2) = 11 x →3 А. lim (x2 + 2) = 11 D. lim (x² – 2) = 11 x -3 X--3 В. lim (x2-2) = -11 x--3 2. Which function becomes undefined? f(x) = 0 C. f(x) = L D. f(x) = ; b= 0 А. В. X = c 3. What is the value of m(x² - 3x +4)? А. С. 2 В. D. 1 4. Which of the following denotes the definition of limit of a function? А. lim f(x) = L C. x approaches c as L В. f(x) approaches L D. lim f (x) = x 5. Graphing the limit of the f(x) = 1 %3D as x approaches to zero, which statement is correct? A. The limit of the function is equal to zero. B. The limit of the function does not exist.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage