Final 4 Solutions

Final 4 Solutions - Create assignment, 57950, Final 1, Dec...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Create assignment, 57950, Final 1, Dec 03 at 4:39 pm 1 This print-out should have 56 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC7b30c 52:04, calculus3, multiple choice, > 1 min, wording-variable. 001 Find the derivative of f when f ( x ) = ‡ e- 2 x 1- 2 x · . 1. df dx = 4 xe- 2 x (1- 2 x ) 2 correct 2. df dx = 8 xe- 2 x (1- 2 x ) 2 3. df dx =- 8 xe- 2 x (1- 2 x ) 2 4. df dx =- 4 xe- 2 x (1- 2 x ) 2 5. df dx = 4 xe- 2 x (1- 2 x ) Explanation: By the product rule df dx = n d dx ‡ 1 1- 2 x e- 2 x ·o = n 2 e- 2 x (1- 2 x ) 2- 2 e- 2 x 1- 2 x o = 2 e- 2 x (1- 2 x ) n 1 1- 2 x- 1 o . Thus df dx = 4 xe- 2 x (1- 2 x ) 2 . CalC7b32b 52:04, calculus3, multiple choice, < 1 min, wording-variable. 002 Find f ( x ) when f ( x ) = e 3 x (cos 4 x + 5 sin 4 x ) . 1. f ( x ) = 3 e 3 x (4 cos 4 x + 20 sin 4 x ) 2. f ( x ) = e 3 x (11 cos 4 x + 23 sin 4 x ) 3. f ( x ) = e 3 x (23 cos 4 x- 11 sin 4 x ) 4. f ( x ) = e 3 x (23 cos 4 x + 11 sin 4 x ) cor- rect 5. f ( x ) = e 3 x (20 cos 4 x- 15 sin 4 x ) 6. f ( x ) = 3 e 3 x (20 cos 4 x- 4 sin 4 x ) Explanation: By the Product and Chain rules, f ( x ) = 3 e 3 x (cos 4 x + 5 sin 4 x ) + e 3 x (20 cos 4 x- 4 sin 4 x ) . Consequently, f ( x ) = e 3 x (23 cos 4 x + 11 sin 4 x ) . CalC7b34a 52:04, calculus3, multiple choice, > 1 min, wording-variable. 003 Find the derivative of f when f ( x ) = 3 2 e 2 x (4 x + 1) 1 / 2 . 1. f ( x ) = 12 xe 2 x (4 x + 1) 1 / 2 2. f ( x ) = 6 xe 2 x (4 x + 1) 3 / 2 Create assignment, 57950, Final 1, Dec 03 at 4:39 pm 2 3. f ( x ) = 12 xe 2 x (4 x + 1) 3 4. f ( x ) = 6 xe 2 x (4 x + 1) 3 5. f ( x ) = 12 xe 2 x (4 x + 1) 3 / 2 correct Explanation: By the product rule f ( x ) = 3 2 n d dx 1 (4 x + 1) 1 / 2 × e 2 x o = 3 2 n- 2 e 2 x (4 x + 1) 3 / 2 + 2 e 2 x (4 x + 1) 1 / 2 o = 3 e 2 x (4 x + 1) 1 / 2 n 1- 1 4 x + 1 o . Thus f ( x ) = 12 xe 2 x (4 x + 1) 3 / 2 . CalC7b43a 52:04, calculus3, multiple choice, > 1 min, wording-variable. 004 Find the x-intercept of the tangent line to the graph of f at the point P (0 ,f (0)) when f ( x ) = e x (3 cos x- 2 sin x ) . 1. x-intercept =- 3 correct 2. x-intercept = 0 3. x-intercept =- 1 4. x-intercept =- 2 5. x-intercept =- 4 Explanation: Since f (0) = 3, the point P = (0 , 3). Now the slope of the tangent line at P is the value of f (0). But f ( x ) = e x (3 cos x- 2 sin x ) + e x (- 3 sin x- 2 cos x ) , in which case f (0) = 1 . By the point-slope formula, therefore, an equation for the tangent line to the graph of f at P is given by y- 3 = ( x- 0) , i.e., y = x + 3 . Consequently, the x-intercept of this tangent line is given by x-intercept =- 3 ....
View Full Document

This note was uploaded on 02/28/2010 for the course M 56200 taught by Professor Radin during the Fall '09 term at University of Texas.

Page1 / 28

Final 4 Solutions - Create assignment, 57950, Final 1, Dec...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online