M408L_HW01 - hyun (hh7953) HW01 gogolev (57440) This...

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

View Full Document Right Arrow Icon
hyun (hh7953) – HW01 – gogolev – (57440) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Determine iF lim x →∞ b ln(5 + 8 x ) - ln(4 + x ) B exists, and iF it does fnd its value. 1. limit = ln 5 4 2. limit = ln 8 correct 3. limit does not exist 4. limit = ln 4 5 5. limit = ln 1 8 Explanation: By properties oF logs, ln(5 + 8 x ) - ln(4 + x ) = ln p 5 + 8 x 4 + x P = ln p 5 /x + 8 4 /x + 1 P . But lim x →∞ 5 /x + 8 4 /x + 1 = 8 . Consequently, the limit exists and limit = ln 8 . 002 10.0 points Determine iF lim x →∞ sin 1 ± 3 + 3 x 5 + 2 x ² exists, and iF it does, fnd its value. 1. limit = π 3 correct 2. limit = π 6 3. limit = π 2 4. limit does not exist 5. limit = π 4 6. limit = 0 Explanation: Since lim x →∞ 3 + 3 x 5 + 2 x = 3 2 , we see that lim x →∞ sin 1 ± 3 + 3 x 5 + 2 x ² exists, and that the limit = sin 1 3 2 = π 3 . 003 10.0 points Determine iF lim x →∞ tan 1 p 3 + x 4 + 3 x P exists, and iF it does, fnd its value. 1. limit = π 4 2. limit = π 3 3. limit = π 6 correct 4. limit = 0
Background image of page 1

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

View Full DocumentRight Arrow Icon
hyun (hh7953) – HW01 – gogolev – (57440) 2 5. limit does not exist 6. limit = π 2 Explanation: Since lim x →∞ 3 + x 4 + 3 x = 1 3 , we see that lim x →∞ tan 1 p 3 + x 4 + 3 x P exists, and that the limit = tan 1 1 3 = π 6 . 004 10.0 points Express the function f ( x ) = sin 2 x + 5 cos 2 x in terms of cos 2 x . 1. f ( x ) = 3 + 2 cos2 x correct 2. f ( x ) = 3 - 2 cos2 x 3. f ( x ) = - 3 + 2 cos 2 x 4. f ( x ) = - 2 - 3 cos 2 x 5. f ( x ) = - 2 + 3 cos 2 x 6. f ( x ) = 2 - 3 cos2 x Explanation: Since sin 2 x = 1 2 (1 - cos 2 x ) , cos 2 x = 1 2 (1 + cos 2 x ) , we can rewrite f ( x ) as f ( x ) = 1 2 (1 - cos 2 x ) + 5 2 (1 + cos 2 x ) . Consequently,
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/18/2010 for the course M 408 L taught by Professor Cepparo during the Fall '08 term at University of Texas at Austin.

Page1 / 8

M408L_HW01 - hyun (hh7953) HW01 gogolev (57440) This...

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