Math 165 - Assignment #8
Name:
Due 8/9/2013
SHOW YOUR WORK!
This assignment covers sections 4,5 and 8 from chapter 6. Make sure you justify your answer clearly! Simply writing
the final result does not mean you receive full credit. You must also show you understand the procedure.
1.- Evaluate the following derivatives or integrals. Choose your u-substitution accordingly such that you make use of
what we know about the antiderivative of the function ax .
q
d
(a)
log5 (10x2 +x )
dx
Z
(b)
0
9
√
7 x
√ dx.
x
Z
(c)
1
3
23x − 2−3x dx.
0
2.- If f (x) = xcos(x) , find f 0 (1).
3.- All living things contain carbon 12 which is stable, and carbon 14, which is radioactive. While a plant or animal
is alive, the ration of these two isotopes of carbon remains unchanged since the carbon 14 is constantly renewed;
after death, no more carbon 14 is absorbed. The half-life of carbon 14 is 5730 years. If charred logs of an old fort
show only 70% of the carbon 14 expected in living matter, when did the fort burn down? Assume that the fort
bunted soon after it was built of freshly cut logs.
4.- Given y = tan−1 ln(4x2 ) , find
dy
dx .
5.- Evaluate the following integrals. Manipulate the integral such that you can use the properties discussed in section
6.8.
Z
1
√
(a)
dx.
12 − 16x2
Z
(b)
2x2
1
dx.
+ 12x + 64