Homework 15-solutions

# Homework 15-solutions - wtm369 Homework 15 Helleloid(58250...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wtm369 Homework 15 Helleloid (58250) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points Find the value of f (- 1) when f ( x ) = 6 tan 1 x- 5 sin 1 x . 1. f (- 1) = correct 2. f (- 1) = 5 2 3. f (- 1) = 3 4. f (- 1) = 3 2 5. f (- 1) = 2 Explanation: Since tan 1 (- 1) =- 4 , sin 1 (- 1) =- 2 , we see that f (- 1) = parenleftBig 5 2- 3 2 parenrightBig = . 002 10.0 points Simplify the expression y = sin parenleftbigg tan 1 x 6 parenrightbigg by writing it in algebraic form. 1. y = x x 2- 6 2. y = x x 2 + 6 3. y = x 2 + 6 6 4. y = x x 2 + 6 correct 5. y = 6 x 2 + 6 Explanation: The given expression has the form y = sin where tan = x 6 ,- 2 &amp;lt; &amp;lt; 2 . To determine the value of sin given the value of tan , we can apply Pythagoras theorem to the right triangle 6 x radicalbig x 2 + 6 From this it follows that y = sin = x x 2 + 6 . Alternatively, we can use the trig identity csc 2 = 1 + cot 2 to determine sin . 003 10.0 points Determine if lim x sin 1 parenleftbigg 1 + x 5 + 2 x parenrightbigg exists, and if it does, find its value. 1. limit = 6 correct 2. limit does not exist 3. limit = 2 4. limit = 4 wtm369 Homework 15 Helleloid (58250) 2 5. limit = 3 6. limit = 0 Explanation: Since lim x 1 + x 5 + 2 x = 1 2 , we see that lim x sin 1 parenleftbigg 1 + x 5 + 2 x parenrightbigg exists, and that the limit = sin 1 1 2 = over 6 . 004 10.0 points Determine the derivative of f ( x ) = 4 sin 1 ( x/ 2) . 1. f ( x ) = 8 1- x 2 2. f ( x ) = 2 4- x 2 3. f ( x ) = 2 1- x 2 4. f ( x ) = 8 4- x 2 5. f ( x ) = 4 1- x 2 6. f ( x ) = 4 4- x 2 correct Explanation: Use of d dx sin 1 ( x ) = 1 1- x 2 , together with the Chain Rule shows that f ( x ) = 4 radicalbig 1- ( x/ 2) 2 parenleftBig 1 2 parenrightBig . Consequently, f ( x ) = 4 4- x 2 . 005 10.0 points Find the derivative of f ( x ) = tan 1 ( e 3 x ) . 1. f ( x ) = 1 1 + e 6 x 2. f ( x ) = 3 1 + e 6 x 3. f ( x ) = 3 1- e 6 x 4. f ( x ) = e 3 x 1- e 6 x 5. f ( x ) = 1 1- e 6 x 6. f ( x ) = 3 e 3 x 1 + e 6 x correct 7. f ( x ) = 3 e 3 x 1- e 6 x 8. f ( x ) = e 3 x 1 + e 6 x Explanation: Since d dx tan 1 x = 1 1 + x 2 , d...
View Full Document

## This note was uploaded on 12/04/2009 for the course M 408k taught by Professor Schultz during the Fall '08 term at University of Texas.

### Page1 / 8

Homework 15-solutions - wtm369 Homework 15 Helleloid(58250...

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

View Full Document
Ask a homework question - tutors are online