MATH 1325 – Final Exam Review, 2026 – Comprehensive study guide
and practice material
The limit of f(x) as x→a describes what happens to f(x) when x is near, but not equal to, the
value a.
A.
This statement is false because the limit of f(x) as x→a describes what happens to f(x) when x is
equal to a.
B.
This statement is false because the limit of f(x) as x→a does not exist for all f(x) and all a.
C.
This statement is false because the limit of x as f(x)→a describes what happens to x when f(x) is
equal to a.
D.
This statement is true because it is part of the definition of the limit. - correct answer ✔✔ D.
This statement is true because it is part of the definition of the limit.
For the limit of f(x) as x→a to exist, the limit from the left and the limit from the right must both
exist and be the same.
A.
This statement is false because one of the limits could be infinity while the other is negative
infinity, so while the one-sided limits exist, the two-sided limit does not exist.
B.
This statement is false because the limit from the left and the limit from the right could both be
infinity or both be negative infinity, so while the one-sided limits do not exist, the two-sided
limit exists.
,C.
This statement is true because it is part of the definition of the existence of a limit.
D.
This statement is false because f(x) must also be defined at x = a. - correct answer ✔✔ C.
This statement is true because it is part of the definition of the existence of a limit.
If f(x) is continuous at x = a then the limit of f(x) as x→a exists and the limit as x→a f(x) = f(a).
A.
The statement is false because it is not necessary for the limit to exist at a given point for a
function to be continuous at that point.
B.
The statement is true because the existence of the limit at a given point and the limit equaling
the function value at that point are conditions for continuity at that point.
C.
The statement is false because a function must be defined at a given point in order for it to be
continuous at that point.
D.
The statement is false because it is not necessary for an existing limit at a given point to equal
the function value at that point for a function to be continuous at that point. - correct answer
✔✔ B.
The statement is true because the existence of the limit at a given point and the limit equaling
the function value at that point are conditions for continuity at that point.
If a function exists at x = a, then the function is continuous at x = a.
A.
, The statement is true because when a function exists at a point, the limit of the function at that
point automatically exists.
B.
The statement is false because there is one other condition necessary for continuity.
C.
The statement is true because when a function exists at a point, the existing limit at that point is
defined to equal the function value at that point.
D.
The statement is false because there are two other conditions necessary for continuity. - correct
answer ✔✔ D.
The statement is false because there are two other conditions necessary for continuity.
An exponential function is continuous everywhere.
A.
The statement is false because only polynomial functions are continuous.
B.
The statement is false because only logarithmic functions are continuous.
C.
The statement is true because an exponential function of the form y = a^x with a positive base
is continuous for all values of x.
D.
The statement is true because an exponential function of the form y = a^x with a negative base
is continuous for all values of x. - correct answer ✔✔ C.
The statement is true because an exponential function of the form y = a^x with a positive base
is continuous for all values of x.
and practice material
The limit of f(x) as x→a describes what happens to f(x) when x is near, but not equal to, the
value a.
A.
This statement is false because the limit of f(x) as x→a describes what happens to f(x) when x is
equal to a.
B.
This statement is false because the limit of f(x) as x→a does not exist for all f(x) and all a.
C.
This statement is false because the limit of x as f(x)→a describes what happens to x when f(x) is
equal to a.
D.
This statement is true because it is part of the definition of the limit. - correct answer ✔✔ D.
This statement is true because it is part of the definition of the limit.
For the limit of f(x) as x→a to exist, the limit from the left and the limit from the right must both
exist and be the same.
A.
This statement is false because one of the limits could be infinity while the other is negative
infinity, so while the one-sided limits exist, the two-sided limit does not exist.
B.
This statement is false because the limit from the left and the limit from the right could both be
infinity or both be negative infinity, so while the one-sided limits do not exist, the two-sided
limit exists.
,C.
This statement is true because it is part of the definition of the existence of a limit.
D.
This statement is false because f(x) must also be defined at x = a. - correct answer ✔✔ C.
This statement is true because it is part of the definition of the existence of a limit.
If f(x) is continuous at x = a then the limit of f(x) as x→a exists and the limit as x→a f(x) = f(a).
A.
The statement is false because it is not necessary for the limit to exist at a given point for a
function to be continuous at that point.
B.
The statement is true because the existence of the limit at a given point and the limit equaling
the function value at that point are conditions for continuity at that point.
C.
The statement is false because a function must be defined at a given point in order for it to be
continuous at that point.
D.
The statement is false because it is not necessary for an existing limit at a given point to equal
the function value at that point for a function to be continuous at that point. - correct answer
✔✔ B.
The statement is true because the existence of the limit at a given point and the limit equaling
the function value at that point are conditions for continuity at that point.
If a function exists at x = a, then the function is continuous at x = a.
A.
, The statement is true because when a function exists at a point, the limit of the function at that
point automatically exists.
B.
The statement is false because there is one other condition necessary for continuity.
C.
The statement is true because when a function exists at a point, the existing limit at that point is
defined to equal the function value at that point.
D.
The statement is false because there are two other conditions necessary for continuity. - correct
answer ✔✔ D.
The statement is false because there are two other conditions necessary for continuity.
An exponential function is continuous everywhere.
A.
The statement is false because only polynomial functions are continuous.
B.
The statement is false because only logarithmic functions are continuous.
C.
The statement is true because an exponential function of the form y = a^x with a positive base
is continuous for all values of x.
D.
The statement is true because an exponential function of the form y = a^x with a negative base
is continuous for all values of x. - correct answer ✔✔ C.
The statement is true because an exponential function of the form y = a^x with a positive base
is continuous for all values of x.
