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Exist Calculus I

The document contains a series of calculus problems and multiple-choice questions related to limits, continuity, derivatives, and the intermediate value theorem. It tests knowledge on concepts such as points of inflection, the behavior of functions, and the evaluation of limits. Each question provides four answer options to choose from.

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melkamu
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50 views2 pages

Exist Calculus I

The document contains a series of calculus problems and multiple-choice questions related to limits, continuity, derivatives, and the intermediate value theorem. It tests knowledge on concepts such as points of inflection, the behavior of functions, and the evaluation of limits. Each question provides four answer options to choose from.

Uploaded by

melkamu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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2

x −9
1. lim ?
x →3 x−3
A. 0 B. 3 C. 6 D. Does not exist
1
2. The function f ( x )= is disconous at:
x−2
A. x=0 B. x=1 C. x=2 D. x=−2
3. The intermediate value theorem guarantees that a function:
A. Is differentiable
B. Is always continous
C. Takes on every value between two function values
D. Is always increasing
4. If f ( x )=x 2 +2 x , what is f ' (2)?
A. 2 B. 4 C. 6 D. 8
5. The second derivative f ' ' (x) determines:
A. The slope of the function.
B. The concavity of the function
C. The x-intercepts of the function
D. The y-values of the function
6. If a particle’s postion is given by s ( t )=t 3 −6 t 2 + 9t , when is it at rest?
A. t=1, t=3
B. t=2, t=4
C. t=0, t=2
D. t=3, t=5
7. If a 10- foot ladder is sliding down a wall at a rate of 2ft/sec, how fast is the bottom moving away
when it is 6 feet from the wall?
A. 2ft/sec.
B. 3ft/sec.
C. 4ft/sec.
D. 5ft/sec.
8. If a function is differentiable at x=a, then it is:
A. Continous at x=a
B. Discotinous at x=a
C. Non-differntiable at x=a
D. Undefined at x=a
9. A point of infection occurs where:
A. f ' ( x )=0 B. f '' ( x )=0 and the concavity changes. C. f ( x )=0 D. f(x) is undefined
10. The area under the curve of a function is calculated using:
A. A derivative
B. A limit
C. An integral
D. A tangent
x
e −x−1
11. Evalute lim 2
x →0 x
A. 0 B. 1 C. 0.5 D. doesnot exist
12. If f (x) is differentiable and f (1)=3 , f (2)=5 , f ' (x)≥ 2, what is the smallest possible value of
f(3)?
A. 7 B. 8 C. 9 D. 10

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