Transcribed Text
In exercises 14, find each limit. Show intermediate steps.
x24

1. lim
x*2
X2 + 5x14 
3x  5x²
2.
lim
2x² +4
3x
3.
lim
x 5+ 5  X
4x  9
4.
lim
x> m
x + 3
3x + 1
5. Find the equation of the line that is perpendicular to the tangent line to the curve, y=
at the point (1,2).
4x  2
In exercises 610, find the derivative of each function. Simplify your result in exercises 7 and 9.
6. y=sin53x =
7. V = e³* (3sin X  cosx)
8. Y = (x + 2) (xx + 3)
9. Y =x2x =
10. y = = sin" (3x) + In
xsec X
11. Given
(x) 
After sketching a graph
a. Find the local maximum and minimum values of f
b. For which values of X is f concave upward?
12. A box with a square base is to have an open top. The area of the material in the box is to be
60 sq in. What should the dimensions be in order to make the volume as large as possible?
13.
A 10foot ladder is leaning against a wall. If a person pulls the base of the ladder away from
the wall at the rate of 1 foot per second, how fast is the top going down the wall when the
base of the ladder is 6 feet from the wall?
In exercises 1417, evaluate the integral.
14. x² 2 + x 3 dx
15. / cos³ X sin X dx
(lnx)³
16.
dx
2
17.
/
x
x  1 dx
1
18. Find the area enclosed by the curves
y=x22x  and y = =2xx²
19. The region bounded by
the parabola y=x², = the line X = 1, and the xaxis
is rotated about the yaxis. Find the volume of the resulting solid.
20.
A
bacteria
culture
starts
with
300
bacteria
and
after
3
hours
there
are
600
bacteria.
Assume
that the bacteria grow at a rate proportional to their size, which means you can use the
function, y = Ae where Y is the number of bacteria and t is time in hours.
a. Find the number of bacteria after 5 hours.
b. When will the population reach 2,000?
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