CALCULUS COMPREHENSIVE QUESTIONS
AND ANSWER LATEST UPLOAD 2024/ 2025
WITH 100% VERIFIED SOLUTIONS
If you want to find the X intercept, cover up the Y as well as its multiple (i.e. if the y were a
6y, then both the 6 and the y would be covered up), and solve for X, and visa versa. -
ANSWER-Describe the cover up method to finding an intercept when the equation of a line
is in standard form.
m equals y2 minus y1 over x2 minus x1 - ANSWER-What is the point slope formula?
Y equals mx plus b - ANSWER-What is the slope intercept formula?
They must have the same slope. - ANSWER-What is required for two lines to be parallel to
each other?
Their slope have to be negative reciprocals of each other. - ANSWER-What is required for
two lines to be perpendicular to each other?
a point and a slope - ANSWER-What two things are needed to make the equation of a line?
It means to approach the limit from the RIGHT side (the positive side of the number line). -
ANSWER-When being asked to evaluate a limit, what does a plus symbol after the limit
mean?
It means to approach the limit from the Left side (the negative side of the number line). -
ANSWER-When being asked to evaluate a limit, what does a negative symbol after the limit
mean?
when adding, subtracting, or multiplying, and even dividing as long as the denominator
doesn't equal zero. - ANSWER-Under what conditions is it okay to separate or combine
limits that are approaching the same number?
, Quite simply, take the limit of the variable, and THEN, raise the limit to the exponent. -
ANSWER-If you have a limit of a variable raised to an exponent, what can you do?
Quite simply plug the number x is approaching into the polynomial and solve. - ANSWER-
When taking the limit of a polynomial of x as x approaches some number, what can you do?
A vertical asymptote - ANSWER-If a zero cannot be factored out at the denominator, what do
you have?
a sign analysis test - ANSWER-What do you do to determine whether or not there is a limit
when an unfactorable zero in the denominator reveals a vertical asymptote?
First, determine the value for x that makes the numerator a zero. Then, pick a number for x
between the zero values for the numerator and denominator; plug the number in, and
determine the sign of the result. Afterwards, plug in a number that is outside the range
previously checked, but on the side of the zero denominator x value. If the two signs match,
the limit exists. Otherwise, the limit does NOT exist. - ANSWER-How is the sign analysis
test performed when an unfactorable zero in the denominator reveals a vertical asymptote?
There is a common factor at that point. - ANSWER-What does it mean when plugging in a x
value results in a zero over zero (0/0)?
Extreme Value Theorem - ANSWER-What theorem states that if f is continuous on [a,b] then
f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at
critical points in the interval or at endpoints of the interval?
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b].
The global extrema occur at critical points in the interval or at endpoints of the interval. -
ANSWER-Define the Extreme Value Theorem.
Critical Number - ANSWER-If f'(c)=0 or does not exist, and c is in the domain of f, then c is
a what? (Derivative is 0 or undefined)
Rolle's Theorem - ANSWER-What theorem states that if we let f be continuous on [a,b] and
differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that
f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval)?
AND ANSWER LATEST UPLOAD 2024/ 2025
WITH 100% VERIFIED SOLUTIONS
If you want to find the X intercept, cover up the Y as well as its multiple (i.e. if the y were a
6y, then both the 6 and the y would be covered up), and solve for X, and visa versa. -
ANSWER-Describe the cover up method to finding an intercept when the equation of a line
is in standard form.
m equals y2 minus y1 over x2 minus x1 - ANSWER-What is the point slope formula?
Y equals mx plus b - ANSWER-What is the slope intercept formula?
They must have the same slope. - ANSWER-What is required for two lines to be parallel to
each other?
Their slope have to be negative reciprocals of each other. - ANSWER-What is required for
two lines to be perpendicular to each other?
a point and a slope - ANSWER-What two things are needed to make the equation of a line?
It means to approach the limit from the RIGHT side (the positive side of the number line). -
ANSWER-When being asked to evaluate a limit, what does a plus symbol after the limit
mean?
It means to approach the limit from the Left side (the negative side of the number line). -
ANSWER-When being asked to evaluate a limit, what does a negative symbol after the limit
mean?
when adding, subtracting, or multiplying, and even dividing as long as the denominator
doesn't equal zero. - ANSWER-Under what conditions is it okay to separate or combine
limits that are approaching the same number?
, Quite simply, take the limit of the variable, and THEN, raise the limit to the exponent. -
ANSWER-If you have a limit of a variable raised to an exponent, what can you do?
Quite simply plug the number x is approaching into the polynomial and solve. - ANSWER-
When taking the limit of a polynomial of x as x approaches some number, what can you do?
A vertical asymptote - ANSWER-If a zero cannot be factored out at the denominator, what do
you have?
a sign analysis test - ANSWER-What do you do to determine whether or not there is a limit
when an unfactorable zero in the denominator reveals a vertical asymptote?
First, determine the value for x that makes the numerator a zero. Then, pick a number for x
between the zero values for the numerator and denominator; plug the number in, and
determine the sign of the result. Afterwards, plug in a number that is outside the range
previously checked, but on the side of the zero denominator x value. If the two signs match,
the limit exists. Otherwise, the limit does NOT exist. - ANSWER-How is the sign analysis
test performed when an unfactorable zero in the denominator reveals a vertical asymptote?
There is a common factor at that point. - ANSWER-What does it mean when plugging in a x
value results in a zero over zero (0/0)?
Extreme Value Theorem - ANSWER-What theorem states that if f is continuous on [a,b] then
f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at
critical points in the interval or at endpoints of the interval?
If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b].
The global extrema occur at critical points in the interval or at endpoints of the interval. -
ANSWER-Define the Extreme Value Theorem.
Critical Number - ANSWER-If f'(c)=0 or does not exist, and c is in the domain of f, then c is
a what? (Derivative is 0 or undefined)
Rolle's Theorem - ANSWER-What theorem states that if we let f be continuous on [a,b] and
differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that
f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval)?
