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REVIEW FOR QUIZ 1 MATH 202 LM SP2014 (5396984)
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Also do the following problems from previous Finals: To get those go to the following
link. http://math.sci.ccny.cuny.edu/courses?name=Math_20200. SPRING 2013: 2(d),
3(ALL); FALL 2012: 1(ALL), 10(a); SPRING 2011: 2(ALL), 9; FALL 2010: 1(ALL), 10;
SPRING 2009: 1(ALL), 7(a); FALL 2008: 1(ALL), 9(a); SPRING 2008: 1(ALL), 9(a).
AND FROM SECTIONS 5.1: EXERCISES: 37, 38 AND 39.
1.
Question Details
SEssCalc2 5.2.023. [2378262]
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SEssCalc2 5.2.034. [2378487]
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SEssCalc2 5.2.040.MI. [2377817]
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SEssCalc2 5.2.053. [2378273]
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SEssCalc2 5.2.061. [2560384]
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Differentiate the function.
G(y) = ln
(2y + 1)4
y2 + 1
G'(y) =
2.
Question Details
Find y' and y''.
y = ln(sec 3x + tan 3x)
y' =
y'' =
3.
Question Details
Find an equation of the tangent line to the curve at the given point.
y = ln(x4 − 624),
4.
(5, 0)
Question Details
Use logarithmic differentiation or an alternative method to find the derivative of the function.
y=
x−2
x8 + 1
y' =
5.
Question Details
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Evaluate the indefinite integral. (Use C for the constant of integration.)
sin 2x
25 + cos2 x
6.
dx
Question Details
SEssCalc2 5.2.059. [2377911]
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SEssCalc2 5.2.058. [2378636]
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SEssCalc2 5.2.057. [2377997]
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SEssCalc2 5.2.055. [2378121]
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SEssCalc2 5.2.062. [2378420]
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Evaluate the integral.
(ln x)8 dx
x
+C
7.
Question Details
Evaluate the integral.
9
x +
8
8.
1
x
2
dx
Question Details
Evaluate the integral.
e
1
9.
5x2 + 6x + 6 dx
x
Question Details
Evaluate the integral.
5
2
10.
dt
4 − 3t
Question Details
Evaluate the integral.
7 cos x dx
6 + sin x
+C
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11.
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Question Details
SEssCalc2 5.3.063. [2377901]
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SEssCalc2 5.3.064. [2378433]
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SEssCalc2 5.3.029. [2377855]
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SEssCalc2 5.4.032.MI. [2378045]
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SEssCalc2 5.4.033. [2377778]
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SEssCalc2 5.4.036. [2378566]
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SEssCalc2 5.4.029. [2378582]
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Evaluate the integral.
ex
6 + ex dx
+C
12.
Question Details
Evaluate the integral.
(6 + ex)2 dx
ex
+C
13.
Question Details
Differentiate the function.
F(t) = e6t sin 2t
F '(t) =
14.
Question Details
Use logarithmic differentiation or an alternative method to find the derivative of the function.
y = x2 cos x
y' =
15.
Question Details
Use logarithmic differentiation to find the derivative of the function.
y = x6 sin x
y' =
16.
Question Details
Use logarithmic differentiation or an alternative method to find the derivative of the function.
y = (sin 7x)ln x
y' =
17.
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Differentiate the function.
y = 2x log6
x
y' =
18.
Question Details
SEssCalc2 5.5.003. [2377939]
-
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has
increased to 410.
(a) Find an expression for the number of bacteria after t hours.
P(t) =
(b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.)
P(4) =
28,258 bacteria
(c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.)
P'(4) =
39,871 bacteria per hour
(d) When will the population reach 10,000? (Round your answer to one decimal place.)
t=
19.
3.3 hr
Question Details
SEssCalc2 5.5.009.MI. [2378596]
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The half-life of cesium-137 is 30 years. Suppose we have a 60-mg sample.
(a) Find the mass that remains after t years.
y(t) =
mg
(b) How much of the sample remains after 130 years? (Round your answer to two decimal places.)
2.98 mg
(c) After how long will only 1 mg remain? (Round your answer to one decimal place.)
t=
20.
177.2 yr
Question Details
SEssCalc2 5.6.017. [2377665]
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SEssCalc2 5.6.019.MI. [2377744]
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Find the derivative of the function. Simplify where possible.
y = (tan−1(4x))2
y' =
21.
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Page 4 of 7
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Find the derivative of the function. Simplify where possible.
y = sin−1(2x + 1)
y' =
22.
Question Details
SEssCalc2 5.6.042. [2378287]
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SEssCalc2 5.6.044. [2378384]
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SEssCalc2 5.6.045. [2377977]
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SEssCalc2 5.6.022. [2378454]
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SEssCalc2 5.7.026. [2535313]
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SEssCalc2 5.7.028. [2378643]
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Evaluate the integral.
√3/9
23.
dx
1 + 81x2
0
Question Details
Evaluate the integral.
π/10
0
24.
sin 5x
1 + cos2 5x
dx
Question Details
Evaluate the integral.
t2
1 − t6
dt
+C
25.
Question Details
Find the derivative of the function. Simplify where possible.
F(θ) = arcsin
sin(9θ)
F '(θ) =
26.
Question Details
Find the derivative. Simplify where possible.
f(x) = tanh(3 + e2x)
f '(x) =
27.
Question Details
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Page 5 of 7
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Find the derivative. Simplify where possible.
g(x) = cosh(ln x)
g'(x) =
28.
Question Details
SEssCalc2 5.7.031. [2377959]
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SEssCalc2 5.7.038. [2377854]
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SEssCalc2 5.7.033. [2377735]
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Find the derivative. Simplify where possible.
y = ecosh(3x)
y'(x) =
29.
Question Details
Find the derivative. Simplify where possible.
y = x tanh−1 x + ln
1 − x2
y'(x) =
30.
Question Details
Find the derivative. Simplify where possible.
f(t) = sech2(3et)
f '(t) =
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Name (AID): REVIEW FOR QUIZ 1 MATH 202 LM SP2014 (5396984)
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