2/3/4. 20 minutes 136.151 Test 2 Oct. 10 2000
Student name: __ Student number: __
Value
1. Evaluate each of the following limits if they exist. If it does not exist, indicate why not.
[5] (a)
[4] (c) 
The following is acceptable: 
It is more precise to notice that since the function 
is not defined when x is a bit less than zero, it follows that the one-sided limit 
does not exist, and so 
does not exist too. If you have done that, you should get the marks.
[8] 2. The graph of the function 
is depicted below. Note that it is undefined at 
and at 
.
[4] (a) Find 
and 
.
; 
[4] (b) What should 
be for the function to be continuous at 
? Explain.
should be 1. Since we would then have 
and the function would be continuous.
[7] 3. Suppose 
. Find 
usin only the definition of the derivative. (Do not use any properties of differentiation; use only the definition of derivative)
.
total
[25]