CALCULUS PRACTICE EXAM
QUESTIONS WITH CORRECT ANSWERS
Apply the definition of the derivative to differentiate the function f(x)=x - ANSWER-1
What is the average rate of change of the function y=2x^2+3 between x=2 and x=4 -
ANSWER-12
Consider the variables p, v, t, and T related by the equations pv=4T, T=100-t, and v=10-
t.
Which of the following is DeltaP for the interval t=0 to t=1? - ANSWER-4
What is the average rate of change of the function y=4x^3-2 between x=2 and x=4? -
ANSWER-112
For which values of k will the line y=x+k meet the parabola of the equation y=-x^2+4x-8
in two distinct points? - ANSWER-K< -23/4
What is the derivative of the function f=2x^2+3 at x=2 - ANSWER-8
The tangent line to the highest point of an open downward parabola (or lowest point of
an open upward parabola) has slope m=0 - ANSWER-TRUE
lim x→2⁻ (lnx)/(x-2) = - ANSWER-Since lnx approaches ln2>0, and the denominator (x-
2) approaches 0, and is negative as x→2⁻, it follows that lim x→2⁻, it follows that lim
x→2⁻ (lnx)/(x-2) = -∞
Finding vertical asymptotes on a graph: - ANSWER-Where ever there is a break in the
graph on the x axis.
Example: x=2 (break at 2 in the graph)
Finding horizontal asymptotes on a graph: - ANSWER-Where ever there is a break in
the graph on the y axis.
Example: y=3 (break at 3 on the graph)
Finding average velocity (Vav) - ANSWER-(b)-(a)/b-a
Finding instantaneous velocity - ANSWER-Plug the time into the equation from finding
the average velocity
Slope of the tangent line - ANSWER-m(tan)= lim h→0: [(a+h)-(a)]/h
QUESTIONS WITH CORRECT ANSWERS
Apply the definition of the derivative to differentiate the function f(x)=x - ANSWER-1
What is the average rate of change of the function y=2x^2+3 between x=2 and x=4 -
ANSWER-12
Consider the variables p, v, t, and T related by the equations pv=4T, T=100-t, and v=10-
t.
Which of the following is DeltaP for the interval t=0 to t=1? - ANSWER-4
What is the average rate of change of the function y=4x^3-2 between x=2 and x=4? -
ANSWER-112
For which values of k will the line y=x+k meet the parabola of the equation y=-x^2+4x-8
in two distinct points? - ANSWER-K< -23/4
What is the derivative of the function f=2x^2+3 at x=2 - ANSWER-8
The tangent line to the highest point of an open downward parabola (or lowest point of
an open upward parabola) has slope m=0 - ANSWER-TRUE
lim x→2⁻ (lnx)/(x-2) = - ANSWER-Since lnx approaches ln2>0, and the denominator (x-
2) approaches 0, and is negative as x→2⁻, it follows that lim x→2⁻, it follows that lim
x→2⁻ (lnx)/(x-2) = -∞
Finding vertical asymptotes on a graph: - ANSWER-Where ever there is a break in the
graph on the x axis.
Example: x=2 (break at 2 in the graph)
Finding horizontal asymptotes on a graph: - ANSWER-Where ever there is a break in
the graph on the y axis.
Example: y=3 (break at 3 on the graph)
Finding average velocity (Vav) - ANSWER-(b)-(a)/b-a
Finding instantaneous velocity - ANSWER-Plug the time into the equation from finding
the average velocity
Slope of the tangent line - ANSWER-m(tan)= lim h→0: [(a+h)-(a)]/h
