1. Consider the piecewise continuous function
, Find:
a. 
b.
c.
d. 
2.
For the function in the graph:
a.
At which value of x does the limit not exist ?
b.
Find 
.
Evaluate the limit.
3. 
4.
Write
down the graphical definition of the derivative of y = f(x) at (xo,
f(xo)).
5. Find the equation of the line tangent to
x3 y2
- y = 2x at x = 1.
6. Differentiate:
a. 
b. y = sin3 4x
c. y = cos (¹/6)
d. 
e. y = ln ( tan x)
7. Evaluate the Integral:
a. 
b.
c. 
d. 
Evaluate the definite Integral
e.
8. Find x & y intercepts,
vertical and horizontal asymptotes, max's, min's, inflection points and sketch
9. Find the area bounded by y = x2
-x , the x axis,
x = 0 , and x - 4
10. A farmer has 600 ft of fencing. He plans to make a rectangular
pen. The pen will be beside a
barn, and one side of the pen will be the barn and hence needs no fencing. Find the dimensions of the pen that
will have maximum area.