AP CALCULUS FINAL REVIEW EXAM
QUESTIONS WITH VERIFIED ANSWERS
Find the limit as x approaches a number. - ANSWER-Plug in the number. If you get 0/0,
factor and cancel then plug in again.
Find the limit as x approaches infinity. - ANSWER-Degree on top greater -> DNE
Degree on bottom greater -> zero
Degrees the same -> ratio of leading coefficients
L'Hopitals Rule for Limits - ANSWER-Take derivative of top and bottom separately, then
plug in number again (repeat until you get an answer, or DNE)
Show that f(x) is continuous. - ANSWER-1) Limit exists (left and right match)
2) Function is defined
3) Limit and function match.
Show that a function is differentiable. - ANSWER-1) Has to be continuous, 2)Cannot
have a cusp
Find the zeros of a function. - ANSWER-Set the equation equal to zero (y=0) and solve
for x.
Find equation of the line tangent to f(x) at (a,f(a)). - ANSWER-Derivative = slope (plug x
into derivative to get m)
y -y1 = m(x-x1)
Find equation of the line normal to f(x) at (a,f(a)). - ANSWER-Normal = perpendicular,
so slope is the negative reciprocal.
Show that f(x) is even - ANSWER-Choose a value for x. Plug in the positive and
negative versions, if it gives you the exact same answer it is even.
Show that f(x) is odd - ANSWER-Choose a value for x. Plug in the positive and negative
versions, if it gives you opposite answers (one is negative) it is odd.
Find the interval where f(x) is increasing/decreasing. - ANSWER-Derivative = 0 or
undefined, Put critical points on sign line, (+) is increasing (-) is decreasing.
Find the relative minimum value of a function f(x). - ANSWER-Find the x-value where
the derivative changes from (-) to (+). Plug back into the function to get the y-value.
Find critical values for a function f(x). - ANSWER-Take derivative, find where it is zero
or undefined.
QUESTIONS WITH VERIFIED ANSWERS
Find the limit as x approaches a number. - ANSWER-Plug in the number. If you get 0/0,
factor and cancel then plug in again.
Find the limit as x approaches infinity. - ANSWER-Degree on top greater -> DNE
Degree on bottom greater -> zero
Degrees the same -> ratio of leading coefficients
L'Hopitals Rule for Limits - ANSWER-Take derivative of top and bottom separately, then
plug in number again (repeat until you get an answer, or DNE)
Show that f(x) is continuous. - ANSWER-1) Limit exists (left and right match)
2) Function is defined
3) Limit and function match.
Show that a function is differentiable. - ANSWER-1) Has to be continuous, 2)Cannot
have a cusp
Find the zeros of a function. - ANSWER-Set the equation equal to zero (y=0) and solve
for x.
Find equation of the line tangent to f(x) at (a,f(a)). - ANSWER-Derivative = slope (plug x
into derivative to get m)
y -y1 = m(x-x1)
Find equation of the line normal to f(x) at (a,f(a)). - ANSWER-Normal = perpendicular,
so slope is the negative reciprocal.
Show that f(x) is even - ANSWER-Choose a value for x. Plug in the positive and
negative versions, if it gives you the exact same answer it is even.
Show that f(x) is odd - ANSWER-Choose a value for x. Plug in the positive and negative
versions, if it gives you opposite answers (one is negative) it is odd.
Find the interval where f(x) is increasing/decreasing. - ANSWER-Derivative = 0 or
undefined, Put critical points on sign line, (+) is increasing (-) is decreasing.
Find the relative minimum value of a function f(x). - ANSWER-Find the x-value where
the derivative changes from (-) to (+). Plug back into the function to get the y-value.
Find critical values for a function f(x). - ANSWER-Take derivative, find where it is zero
or undefined.
