In exercises 1-4, find each limit. Show intermediate steps.
X2 + 5x-14 -
3x - 5x²
x 5+ 5 - X
4x - 9
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 6-10, 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
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?
A 10-foot 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 14-17, evaluate the integral.
14. x² 2 + x 3 dx
15. / cos³ X sin X dx
x - 1 dx
18. Find the area enclosed by the curves
y=x2-2x - and y = =2x-x²
19. The region bounded by
the parabola y=x², = the line X = 1, and the x-axis
is rotated about the y-axis. Find the volume of the resulting solid.
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?
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.