A2_f2015.pdf

# A2_f2015.pdf - MATH 1500 D01/D02 Fall 2015 Assignment 2...

• 2

This preview shows pages 1–2. Sign up to view the full content.

MATH 1500 D01/D02 Fall 2015 Assignment 2 SHOW ALL WORK to get full marks. Leave answers as exact answers. For example, leave it as 1 { 7 as opposed to 0 . 142857 . Word problems should have sentence answers with units. This assignment covers sections from 2.5–2.8 and 3.1–3.2. Use the definition of derivative ONLY for Q5. Do not use the definition of derivative in any other questions. 1. [7] Use limits to calculate a and b such that the following function is continuous for all real numbers x. f p x q “ \$ & % sin ´ π 2 x ¯ ` ax 2 ` b x ă 2 3 x 2 e p x ´ 2 q ` a ` b ` ln p x ´ 1 q x ą 2 2. [4] Show that sin ´ πx 2 ¯ 6 x ´ 4 has a solution on the interval p 0 , 1 q . Justify your answer. 3. Evaluate the following limits: (a) [4] lim x Ñ´8 ˆ e x ` 1 ` x 2 9 x 2 ´ 7 ˙ . (b) [4] lim x Ñ´8 ? x 6 ´ x ` 1 2 x 3 ´ 1 . (c) [5] lim x Ñ8 ` 2 x ´ ? x 2 ` 1 ˘ . 4. [6] Use limits to determine all horizontal and vertical asymptotes for the function f p x q “ ? x 2 ` 1 ´ x ` 1 . 5. [7] Use the definition of the derivative to calculate the derivative of the function f p x q “ 1 x 2 ` x ` 1 . 1

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

6. Calculate the derivative of the following functions. Do not simplify your answers.
This is the end of the preview. Sign up to access the rest of the document.
• Fall '10
• ThomasKucera

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern