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| 1.
Answer E |
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| 2. This problem requires
L'Hopital's Rule. Since the numerator and denominator of the original
fraction each approach zero we can look at the limit of the quotient of the
numerator over the quotient of the denominator:
Answer C |
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| 3. Using substitution:
Answer A |
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| 4.
Answer D |
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5.
 The
tangent line through (1,2) is y=3(x-1)+2
Moving along this tangent line 0.5 in the x-direction means we are using
x=1.5. The approximation of f(1.5) is y=3(1.5-1)+2 or 3.5.
We are now at the point (1.5,3.5)
Moving along this new tangent line 0.5 in the x-direction means we are
using x =2. The new tangent line will be y =5(x-1.5)+3.5. The
approximation of f(2) along this tangent line is y = 5(2-1.5)+3.5 or 6
Answer C |
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6.
 can be
thought of a integral of a p-series.We know that this integral will
converge if 2p>1 or p>1/2.
Answer C |
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| 7.
The particle is at rest when
 .
This occurs when
The only time the particle is at rest in both directions is at time t =
2.
Answer C |
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| 8.
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| Answer B |
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| 9.
Answer A |
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| 10.
which is a geometric series with a = 2/3 and r = 2/3.
So the sum is
 or the
first sum is 2 x 2 or 4.
Answer C |
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| 11.
Answer D |
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12.
 Answer E |
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| 13.
At point a the graph is continuous, but not differentiable because the
limit of the difference quotient for slopes does not exist at this point.
Answer A |
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| 14. From the slopefield we
can notice some characteristics: when x=0 the slope is always zero
All slopes in the fourth quadrant are positive.
This statement rules out: A, C, and D.
Now notice that all the slopes in the second quadrant are negative.
This rules out B
This leaves only E.
Answer E |
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15. If
 is the length of the curve we know that
 . The antiderivative of f '(x) is
 . This describes a family of
curves. Since the point (1,6) in contained on the graph, we'll
substitute this point in the family to solve for C.
Answer B |
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| 16.
The tangent line has a slope of 3 so this is the slope of the function f
at -1.
Answer C |
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| 17.
The equation would be x=-3.
Answer A |
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| 18.
Answer C |
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| 19. f ' (x)=2x+3 and
f(1)=2
Answer D |
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| 20.
Answer D |
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| 21.
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Answer B
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| 22.
We know that
converges for p>1 so by the comparison test
 converges
for p-1>1or p>2.
Answer E |
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| 23.
Answer B |
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| 24.
I.
II.
III.
Answer D |
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| 25.
Answer D |
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| 26.
Answer D |
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| 27.
Answer E |
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| 28.
Answer D |
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