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This is the Exam of Calculus which includes Types of Concavity, Points of Inflection, Maxima and Minima, Possible Features, Asymptotes, Critical Points, Function, Material etc. Key important points are: Represent Derivatives, Limits, Simplify, Integrals, Evaluate, Function, Maxima, Minima, Asymptotes, Function Increasing
Typology: Exams
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Read each problem carefully. Show your work clearly. No calculators. (If you need more space, please use the back of the previous page and label clearly).
a)
3 3 0
lim h h h
b) 6
sin( ) 1 lim^2
6
x
x
x
d) tan( xy ) y^2 2 x
f)
3
0
x y e dtt
a) cos (^4 ) x x x dx x
b)
1/
1/2 1 2
dx x
c)
(^3 )
2 ^2 x^ ^5 dx
d)
2 4/
sec 3 tan
x dx x
(^)
asymptotes.
Maxima: _____________________________
Minima:______________________________
Horizontal Asymptote(s): ________________
Vertical Asymptote(s): __________________
Slant Asymptote(s):_____________________
Points of inflection _____________________
b) Use one step of Newton’s Method with initial guess x 0 (^) 8 to approximate a root of y 12 x x^2.
seconds (where t 0 ). At what time(s) does the particle stop moving for an instant?
a. Approximate the area under the curve
y x
on the interval [2, 8] by using three
rectangles of equal width and the value of the function at the left-hand endpoint of each interval. Is your result an underestimate or overestimate of the true area under the curve? Justify.
b. Use an integral to evaluate the area under the curve y^4 x
on the interval [2, 8].
c. Set up an integral in dx for the area enclosed by the curves y x^2^ and y 3 x. DO NOT EVALUATE.
d. Set up an integral in dy for the same area as in part c. DO NOT EVALUATE.
