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The function, f(x) = √1 + 9x² over the interval 0≤x≤1 (a) Find f'(x). Fully simplify your answer. (b) Write the equation of the line tangent to fat x = 3. Fully simplify all numeric values. (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 3 1/3 (d) Find the value of f answer. dx (f(x))² (f(x); 0≤x≤ // 3x√√2;=

The function, f(x) = √1 + 9x² over the interval 0≤x≤1 (a) Find f'(x). Fully simplify your answer. (b) Write the equation of the line tangent to fat x = 3. Fully simplify all numeric values. (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 3 1/3 (d) Find the value of f answer. dx (f(x))² (f(x); 0≤x≤ // 3x√√2;=

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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The function, f(x)=√1 + 9x² over the interval 0 ≤ x ≤ 1 (a) Find f'(x). Fully simplify your answer. 1 (b) Write the equation of the line tangent to fat x =. Fully simplify all numeric values. (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 3 ƒ(x); 0 ≤ x ≤ ²}/ 3x √2; < x≤ 1 < •1/3 (d) Find the value of f dx Fully simplify your answer. (f(x))² (e) Let g(x) = ſtan²x √1 +9t² dt over the interval 0 ≤ x ≤. Find g′ (7). Fully simplify your answer.
Transcribed Image Text:The function, f(x)=√1 + 9x² over the interval 0 ≤ x ≤ 1 (a) Find f'(x). Fully simplify your answer. 1 (b) Write the equation of the line tangent to fat x =. Fully simplify all numeric values. (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 3 ƒ(x); 0 ≤ x ≤ ²}/ 3x √2; < x≤ 1 < •1/3 (d) Find the value of f dx Fully simplify your answer. (f(x))² (e) Let g(x) = ſtan²x √1 +9t² dt over the interval 0 ≤ x ≤. Find g′ (7). Fully simplify your answer.
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