Math 1100 Section 4 Test1
Name:
Read all directions carefully and show all your work for full credit.
Do the rst 9 problems (10 pts each) on the exam and then choose one of the last
three (15 points) to do. Your score on the exam will then be taken out of 100 points.
Do not simplify your answers unless otherwise specied. Good Luck!!!
1. If ( ) =
f x
p
x
5 and ( ) =
g x
2 + 2x 35
x
2. Find lim
!5 x2 25
x
3
x
+ 17 then nd ( (2)) and ( (9))
f g
g f
Ix
3. Say ( ) = 2 5+6 66 . Is ( ) continuous on the whole real line? If ( )
has any discontinuities determine where they are and of what type they are.
x
x
4. If ( ) = 17 10
point (1 11).
P x
x
;
x
15
x
I x
I x
+ 20 then nd the equation for the tangent line at the
5. Remembering that
=
nd the Revenue function and
the marginal Revenue given that the cost function is ( ) = 50 2 + 10 16
and the prot function is ( ) = 15 3 6 + 5
P rof it
Revenue
C ost
C x
P x
x
x
p3 1
6. If T (x) = ( x + )(7x + 6) nd
4
x
T
0
( )
x
x
x
7. If
p
D(x) = 5 +6 nd
x
p
x
D
0
( ).
x
8. If ( ) = 11 5 + 6 nd ( ).
E x
x
E
0
x
9. Using the limit denition of the derivative nd ( ) where
V
0
x
V (x) = 4 3+7 .
x
10. Use the limit denition of the derivative to nd ( ) where
K
0
x
K (x) = p61+9 .
x
11. If
W (x) =
x
p 2
p11 +1 nd
3 +6
87
4
x
x
W
0
( )
x
12. Jacob is standing on a cli and throws a ball straight up. The height of the ball
seconds after Jacob throws the ball is given by the function ( ) = 10 2 + +
where 2 R. If the velocity of the ball after 1 9 seconds is zero and the ball
lands on the earth after 5 seconds (H(5)=0) then nd and . How fast was
the ball going when it hit the ground?
t
H t
b; c
t
:
b
c
bt
c
1. (10pts)
2. (10pts)
3. (10pts)
4. (10pts)
5. (10pts)
6. (10pts)
7. (10pts)
8. (10pts)
9. (10pts)
10. (15pts)
11. (15pts)
12. (15pts)
total