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Problem [1] Given f(x) = sinx a. Find P" (x) b. Show [f'(x) = f(x)

Problem [1] Given f(x) = sinx a. Find P" (x) b. Show [f'(x) = f(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Part I: The integral is called the anti-derivative Part II: If F(x) is an anti-derivative, then Let f be a continuous function on la, b). Then d = S(1) = f(x) dx f(2)dz = F(b) – F(a) a Where F is any antiderivative of f. "The dertvative of the integral returns the function, f(x) over [ax] ". Thus integration and dervative are inverse functions. Def: Anti-derivatives Def: i) [ f(x) dx = F(x) + C we call F(x) an anti-derivative. ii) If F(x) is an anti-derivative, then F'(x) = f(x) Problem [1] Given f(x) = sinx a. Find f" (x) b. Show [f'(x) = f(x) Problem [2] a) Define F(x) = e + 1 dt Find F'(x)
Transcribed Image Text:Part I: The integral is called the anti-derivative Part II: If F(x) is an anti-derivative, then Let f be a continuous function on la, b). Then d = S(1) = f(x) dx f(2)dz = F(b) – F(a) a Where F is any antiderivative of f. "The dertvative of the integral returns the function, f(x) over [ax] ". Thus integration and dervative are inverse functions. Def: Anti-derivatives Def: i) [ f(x) dx = F(x) + C we call F(x) an anti-derivative. ii) If F(x) is an anti-derivative, then F'(x) = f(x) Problem [1] Given f(x) = sinx a. Find f" (x) b. Show [f'(x) = f(x) Problem [2] a) Define F(x) = e + 1 dt Find F'(x)
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