Calculus II 
Quiz #1 
February 15, 2002
Name____________________    
R.  Hammack 
Score ______

(1)   Find the following antiderivatives.

(a)  [Graphics:Images/quiz1solved_gr_1.gif][Graphics:Images/quiz1solved_gr_2.gif]



(b)  [Graphics:Images/quiz1solved_gr_3.gif][Graphics:Images/quiz1solved_gr_4.gif]



(c) [Graphics:Images/quiz1solved_gr_5.gif]



(d)   [Graphics:Images/quiz1solved_gr_6.gif]

[Graphics:Images/quiz1solved_gr_7.gif]
[Graphics:Images/quiz1solved_gr_8.gif]
[Graphics:Images/quiz1solved_gr_9.gif]

(e) [Graphics:Images/quiz1solved_gr_10.gif]

[Graphics:Images/quiz1solved_gr_11.gif]
[Graphics:Images/quiz1solved_gr_12.gif]
[Graphics:Images/quiz1solved_gr_13.gif]

(2)  The graph of a function f(x) has slope [Graphics:Images/quiz1solved_gr_14.gif]  at each point (x, f(x)).
Also, the graph of  f(x) passes through the point (1, 5).  Find the function f(x).

The information says slope = f '(x) = [Graphics:Images/quiz1solved_gr_15.gif].
This means  f(x) =[Graphics:Images/quiz1solved_gr_16.gif]
[Graphics:Images/quiz1solved_gr_17.gif].
Thus f(x) = [Graphics:Images/quiz1solved_gr_18.gif]
To determine f completely, we just need to find C. To do this, use the fact that f(1)=5.
5=f(1)= [Graphics:Images/quiz1solved_gr_19.gif]
5= 0 + 3/4 +C
Therefore C = 17/4, and  the answer to the question is f(x) = [Graphics:Images/quiz1solved_gr_20.gif]