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1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of F(x) = [** f(t) dt. -2 ii. Verify that F'(x) = f(x) and F(-2) = 0.

1) Consider the functions ƒ(a) = 100 – 2¹ª and F(x) = f(t 1² f(t) dt. i. Write a simplified form of F(x) = [** f(t) dt. -2 ii. Verify that F'(x) = f(x) and F(-2) = 0.

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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4 a) Consider the functions f(x) = 100 – xª and F(x) i. Write a simplified form of F(x) = f*"¸ ƒ(t) dt. -2 ii. Verify that F'(x) = f(x) and F(-2) = 0. = [₁, f(t) f(t) dt. b) Now consider the function g(x) √100 x4. Unlike the previous function, there is no closed- form "nice" way to write the anti-derivative G(x) where G'(x) = g(x). = Instead, use the Fundamental Theorem of Calculus Part II to find an integral-defined function G(x) such that Gʻ(x) = g(x) and G(−2) = 0.
Transcribed Image Text:4 a) Consider the functions f(x) = 100 – xª and F(x) i. Write a simplified form of F(x) = f*"¸ ƒ(t) dt. -2 ii. Verify that F'(x) = f(x) and F(-2) = 0. = [₁, f(t) f(t) dt. b) Now consider the function g(x) √100 x4. Unlike the previous function, there is no closed- form "nice" way to write the anti-derivative G(x) where G'(x) = g(x). = Instead, use the Fundamental Theorem of Calculus Part II to find an integral-defined function G(x) such that Gʻ(x) = g(x) and G(−2) = 0.
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