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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 = . Fully simplify all numeric values. 3 (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 【(d) Find the value of £¹/³ (f(x); 0≤x 3 3x√2; < x≤ 1 dx (f(x))² (e) Let g(x) = 0.2 answer. Fully simplify your answer. tan²x √1 +9t² dt over the interval 0 ≤ x ≤ Find g' Fully simplify your

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 = . Fully simplify all numeric values. 3 (c) Let g be the function defined by Is g continuous at x = ? Use the definition of continuity to justify your answer. 【(d) Find the value of £¹/³ (f(x); 0≤x 3 3x√2; < x≤ 1 dx (f(x))² (e) Let g(x) = 0.2 answer. Fully simplify your answer. tan²x √1 +9t² dt over the interval 0 ≤ x ≤ Find g' Fully simplify your

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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See the attached Calculus problem. Please help with parts C, D, and E. Thank you.

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.
Expert Solution
Step 1

Given: A function fx=1+9x2 over the interval 0≤x≤1

To Find: 

c) Let g be a function defined by fx0≤x≤133xx13≤x≤1 . is g is continuous?

d) Value of ∫01/3dxfx2.

e) Let gx=∫0.2tan2x1+9t2dt over the interval 0≤x≤π3. Evaluate g'π4.

 

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