{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW2 - Problem 4(5 points Using the deﬁnition of the...

This preview shows page 1. Sign up to view the full content.

MATH 102, ASSIGNMENT 2 DUE MAY 26 Problem 1. (5 points) a) Find the vertical asymptotes (if any) for each of the following functions: F 1 ( x ) = x 2 + 1 + 1 x , F 2 ( x ) = x 2 + 1 - 1 x b) Which of the following functions has horizontal asymptotes? Why? α ( x ) = 3 x 2 + 1 2 x 3 - 1 , β ( x ) = 3 x 3 + 1 2 x 2 - 1 , γ ( x ) = 3 x 2 + 1 2 x 2 - 1 Problem 2. (5 points) Find a and b such that the following function is continuous: f ( x ) = x 2 + b , if x < 0 a , if x = 0 x 2 - b , if x > 0 Problem 3. (5 points) a) Using the limit definition, show that the absolute value function f ( x ) = | x | is not differentiable at 0. b) Sketch the graph of a function which is continuous at -2, 0, and 2, but not differentiable at any one of these three points.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem 4. (5 points) Using the deﬁnition of the derivative, ﬁnd f ( x ) for f ( x ) = x-2 . Then ﬁnd the equation of the tangent line to the graph of f at the point where x = 1. Problem 5. (5 points) Using the deﬁnition of the derivative, ﬁnd g ( ) for g ( s ) = 1 √ s + 1 . J-RULE: Just answers - “yes”, “5” - won’t get you full marks, but (correctly) justiﬁed answers - “yes, because. ..”, “(some algebra). .. (sweat sweat) . .. 5” - will. 1...
View Full Document

{[ 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