or
if appropriate for your answers.
Math 2253 Test #1 No Calculator Allowed
1. Evaluate the limits. Use or
if appropriate for your answers.
a) 
b) 
c)
d) 
e)
f)
g)
2. True or false: If
= 9, and
, then
is continuous at x = 2.
3. Evaluate the limits. Use
and
if appropriate.
a) 
b)
4. Use your answers from problem 3 to find the equation of the horizontal asymptotes, if any, for the graphs of:
a) 
b)
5. If
= 4, and if
= 1, calculate:
a)
b) 
c)
6. On what intervals is the function tan x continuous?
7. Recall that the derivative of the function
is defined as
.
a) Use this definition to calculate
for
.
b) Use your answer from part a) to find
.
c) What is the equation of the tangent line to the graph of
at the point (-2,10)?
8. For each function, determine all values of x for which the function is not continuous, and then describe the
behavior of the graphs of the functions at these x-values.
a) 
b)
9. The graph of G(x) is pictured. Use the graph to approximate the limits and answer the questions.
Use 
or
if it is appropriate for your answers.
a) 
b)
c)
d)
e) 
f)
g)
h)
i) For what values of x is G(x) not continuous?
j) For what values of x is G(x) not differentiable?
10. If 
, what is
?