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

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

View Full Document Right Arrow Icon
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.
Background image of page 1
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

This note was uploaded on 07/31/2011 for the course MATH 102 taught by Professor Maryamnamazi during the Spring '10 term at University of Victoria.

Ask a homework question - tutors are online