MATH 105 Practice Problems to Work Before Test One
2
lim 3
1) Find x 2( x x + 7 x 4)
12 x 2 + 11x 15
x 0.75 4 x 2 + 5 x 6
2) Find lim
4x2 + 2x 2
x 0.5 8 x 2 + 6 x + 1
3) Find lim
4) Use the graph of y = f (x) given below to find the following limits.
lim
PROBLEM 1 : Find two nonnegative numbers whose sum is 9 and so that the
product of one number and the square of the other number is a maximum.
PROBLEM 2 : Build a rectangular pen with three parallel partitions using 500
feet of fencing. What dimensions
MATH 105 Practice Problems to Work Before The Final
In problems 1-4, find the indefinite integral.
1
1)
2)
( x
3)
4)
x
e
3
6
+
1
+ 9 3 x 4 + e 3 x dx
3x
)
3 x 4 + 6 x + 1) 5 (5 x 5 10 x 3 + 5) dx
x
3
14 x 3 7 x
dx
x4 x2 + 3
x2
dx
2
5) Approximate the
MATH 105 Practice Problems to Work Before Test Two
In problems 1-10, compute the derivative of the given function.
1) f ( x) = (3 x 2 4) 4 6 x 1
2) g ( p ) =
3) s (t ) =
4) f ( x) =
( p + 4)( p 3)
2p+ 5
4t + t 3
t+ 7
3
2
3
7) h( x ) = ln(4 x + 7)
7
8) v (
MATH 105 Practice Problems to Work Before Test Three
In problems 1-5, find each of the following: a) all intervals on which the function is increasing; b) all
intervals on which the function is decreasing; c) all intervals on which the function is concave
Name_
Example:
The weekly demand for the ABC color flat screen TV is p =
where p denotes the
600 ` .05 x ; 0 x 12,000
wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated
with manufacturing the TV