Josephood7

Consider the function [math] whose graph is shown below.

This function is given by [math]

(a) Find a formula for the single variable function [math].
[math] 
What is [math] for this function?
[math] 
Find its limit as [math]:
[math] 

(b) Based on your work in (a), is the single variable function [math] continuous?  ? yes no 

(c) Next, similarly consider [math].
[math] 

[math] 
[math] 

(d) Based on this work in (a), is the single variable function [math] continuous?  ? yes no 

(e) Finally, consider [math] along rays emanating from the origin. Note that these are given by [math], for some (constant) value of [math].

Find and simplify [math] on the ray [math]:
[math] 

(Notice that this means that [math] is a contour of [math]. Be sure you can explain why this is.)

Find and simplify [math] on any ray [math].
[math] 

(Again, notice that this means that any ray [math] is a contour of [math]; be sure you can explain why.)

(f) Is [math] continuous at [math]?  ? yes no 

Find the limit, if it exists, or type N if it does not exist.

[math] 

 Find the limit of the function [math] as [math]. Assume that polynomials, exponentials, logarithmic, and trigonometric functions are continuous. [Hint: [math].]

[math] 
(Enter DNE if the limit does not exist.)

 For the function [math] below, determine whether there is a value for [math] making the function continuous everywhere. If so, find it. [math]

[math] 
(If there is no value of [math] that works, enter none, and be sure that you can explain why there is no such value.)

(1 point)
The largest set on which the funtion [math] is continuous is 

A. [math]
B. [math]
C. the whole xy-plane
D. [math]
E. [math]

Find the limit (enter 'DNE' if the limit does not exist)
Hint: rationalize the denominator. [math]