AP Calculus BC
ID: 4
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#TOP10+1
Evaluate each limit. Use L'Hôpital's Rule if it can be applied. If it cannot be applied, evaluate
using another method and write a * next to your answer.
ex - 1
1) lim
x®0
4x3
For each problem, find the average rate of change of the function over the given interval.
4
3
2) g(t) = -2t 2 + 2; [1, ]
Solve each related rate problem.
3) A conical paper cup is 10 cm tall with a radius of 10 cm. The bottom of the cup is
punctured so that the water level goes down at a rate of 2 cm/sec. At what rate is the
volume of water in the cup changing when the water level is 8 cm?
Worksheet by Kuta Software LLC
-1-
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For each problem, find the equation of the line tangent to the function at the given point. Your
answer should be in slope-intercept form.
4) h( x) =
2
at (1, 1)
x+1
For each problem, use the method of cylindrical shells to find the volume of the solid that
results when the region enclosed by the curves is revolved about the the given axis. Set up, but
do not evaluate the integral.
5) y = 2 x + 2, y = x 2 + 2
Axis: x = 3
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
Worksheet by Kuta Software LLC
-2-
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For each problem, find the volume of the solid that results when the region enclosed by the
curves is revolved about the the given axis. Set up, but do not evaluate the integral.
6) y = ( x + 4) 2, y = 1, x = -4, x = -3
Axis: x = 1
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
For each problem, approximate the area under the curve over the given interval using 3
trapezoids.
7) f = -
x2
+ 6; [-3, 0]
2
For each problem, find F' ( x).
x3
8) F ( x) =
ò
(t 3 - t 2 - 4) dt
-1
Worksheet by Kuta Software LLC
-3-
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For each problem, find the particular solution of the differential equation that satisfies the initial
condition.
9) y' = e x - y, y(1) = ln (e + 3)
For each problem, you are given a table containing some values of differentiable functions f ( x)
, g( x) and their derivatives. Use the table data and the rules of differentiation to solve each
problem.
10) x
f ( x)
1
4
2
3
3
4
f ' ( x) g( x) g' ( x)
-1
3
2
3
-1
2
-1
1
0
1
3
2
3
Part 1) Given h1( x) = f ( x) × g( x), find h1' (3)
f ( x)
Part 2) Given h2( x) =
, find h2' (2)
g( x)
Part 3) Given h3( x) = ( f ( x)) 2, find h3' (1)
Part 4) Given h4( x) = f ( g( x)), find h4' (2)
1
2
2
Evaluate each indefinite integral using integration by parts.
11)
ò
2
x 3 e x dx
Worksheet by Kuta Software LLC
-4-
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