MAE 101 PT1 UPDATED ACTUAL Exam
Questions and CORRECT Answers
From the graph of y = f(x), how do we obtain the graph of y = f(x-2) +3? - CORRECT
ANSWER - Shift to the right by 2, and then shift up by 3
Given that lim g(x) = 7, and lim(2f(x) - 3g(x)) = 1 evaluate the limit - CORRECT ANSWER -
11
For what value of the constant c is the function f continuous on
cx + 7 for x <= 2
cx^2 - 5 for x > 2 - CORRECT ANSWER -6
The cost (in dollars) of producing x units of a certain commodity is C(x) = 4,280+13x+0.03x2.
Find the average rate of change with respect to x when the production level is changed from x =
102 to x = 118. - CORRECT ANSWER - 19.6
Find the first and the second derivatives of the function.
G(r) = sqrt(r) + 5sqrt(r) - CORRECT ANSWER - \frac{1}{2}r^{-1/2}+\frac{1}{5}r^{-4/5},
\,\frac{-1}{4}r^{-3/2}-\frac{4}{25}r^{-9/5}
Calculate y'(1). - CORRECT ANSWER - (cos 1 - sin 1)/2
Find y' by implicit differentiation 8 cos x sin y = 7 - CORRECT ANSWER - tan(x)tan(y )
The radius r of a sphere is increasing at the rate of 0.2 (cm/s). At what rate (in cm3/s) is the
volume V of the sphere increasing when r = 3cm?
Round your answer to 2 decimal places. - CORRECT ANSWER - 22.62
, Find the absolute minimum value(s) of y=2x2-20x+9 on the interval [0, 6]. - CORRECT
ANSWER - -41
Find the minimum of the product of two numbers with the property that the first minus 4 times
the second is 20. - CORRECT ANSWER - None of the other choices is correct
Use Newton's method with the specified initial approximation x1 to find x3, the third
approximation to the root of the given equation.
cos x = x - 4, x1=3.1
(Give your answer to four decimal places) - CORRECT ANSWER - 3.0088
A particle moves along a straight line with velocity function v(t)=2sin t - 4cos t and its initial
displacement is s(0) = 4. Find its position function. - CORRECT ANSWER - s(t)=6-2cos t-
4sin t
Use the Right-endpoint Rule with n = 4 to approximate the integral.
3 + t^2 - CORRECT ANSWER - 42
Use the Midpoint Rule with n = 3 steps to estimate the integral
x 2 2.5 3 3.5 4 4.5 5
f(x) 4 5 6 10 8 9 7 - CORRECT ANSWER - 24
If 2x - 1 < fx < x^2 for 0 < x < 3, find lim fx - CORRECT ANSWER -1
Simplify [f(x+h)-f(x)] / h for f(x) = -3x2 +x - CORRECT ANSWER - -6x-3h+1
Questions and CORRECT Answers
From the graph of y = f(x), how do we obtain the graph of y = f(x-2) +3? - CORRECT
ANSWER - Shift to the right by 2, and then shift up by 3
Given that lim g(x) = 7, and lim(2f(x) - 3g(x)) = 1 evaluate the limit - CORRECT ANSWER -
11
For what value of the constant c is the function f continuous on
cx + 7 for x <= 2
cx^2 - 5 for x > 2 - CORRECT ANSWER -6
The cost (in dollars) of producing x units of a certain commodity is C(x) = 4,280+13x+0.03x2.
Find the average rate of change with respect to x when the production level is changed from x =
102 to x = 118. - CORRECT ANSWER - 19.6
Find the first and the second derivatives of the function.
G(r) = sqrt(r) + 5sqrt(r) - CORRECT ANSWER - \frac{1}{2}r^{-1/2}+\frac{1}{5}r^{-4/5},
\,\frac{-1}{4}r^{-3/2}-\frac{4}{25}r^{-9/5}
Calculate y'(1). - CORRECT ANSWER - (cos 1 - sin 1)/2
Find y' by implicit differentiation 8 cos x sin y = 7 - CORRECT ANSWER - tan(x)tan(y )
The radius r of a sphere is increasing at the rate of 0.2 (cm/s). At what rate (in cm3/s) is the
volume V of the sphere increasing when r = 3cm?
Round your answer to 2 decimal places. - CORRECT ANSWER - 22.62
, Find the absolute minimum value(s) of y=2x2-20x+9 on the interval [0, 6]. - CORRECT
ANSWER - -41
Find the minimum of the product of two numbers with the property that the first minus 4 times
the second is 20. - CORRECT ANSWER - None of the other choices is correct
Use Newton's method with the specified initial approximation x1 to find x3, the third
approximation to the root of the given equation.
cos x = x - 4, x1=3.1
(Give your answer to four decimal places) - CORRECT ANSWER - 3.0088
A particle moves along a straight line with velocity function v(t)=2sin t - 4cos t and its initial
displacement is s(0) = 4. Find its position function. - CORRECT ANSWER - s(t)=6-2cos t-
4sin t
Use the Right-endpoint Rule with n = 4 to approximate the integral.
3 + t^2 - CORRECT ANSWER - 42
Use the Midpoint Rule with n = 3 steps to estimate the integral
x 2 2.5 3 3.5 4 4.5 5
f(x) 4 5 6 10 8 9 7 - CORRECT ANSWER - 24
If 2x - 1 < fx < x^2 for 0 < x < 3, find lim fx - CORRECT ANSWER -1
Simplify [f(x+h)-f(x)] / h for f(x) = -3x2 +x - CORRECT ANSWER - -6x-3h+1
