Test Your Calculus Knowledge

Test Your Calculus Knowledge

Take this quiz to see how well you understand the concepts and principles of calculus.

published on September 08, 2023
1/12

What is the limit of the function f(x) = 3x^2 + 5x - 2 as x approaches 2?

What is the limit of the function f(x) = 3x^2 + 5x - 2 as x approaches 2?
9
19
-19
17
2/12

What is the derivative of the function f(x) = 4x^3 - 2x^2 + 5x - 3?

What is the derivative of the function f(x) = 4x^3 - 2x^2 + 5x - 3?
12x^2 - 4x + 5
12x^2 - 4x + 1
12x^2 - 4x + 6
12x^2 - 4x - 2
3/12

What is the integral of the function f(x) = 2x^2 + 3x + 1?

What is the integral of the function f(x) = 2x^2 + 3x + 1?
2/3x^3 + 3/2x^2 + x
3/4x^3 + 4/3x^2 + x
3/5x^3 + x^2 + x
2/5x^3 + 2/3x^2 + x
4/12

What is the product rule in calculus used for?

What is the product rule in calculus used for?
Differentiating a product of two functions
Finding the limit of a function
Integrating a function
Differentiating a quotient of two functions
5/12

Which theorem in calculus states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a)?

Which theorem in calculus states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the open interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a)?
Fundamental Theorem of Calculus
Mean Value Theorem
Intermediate Value Theorem
L'Hopital's Rule
6/12

Which of the following functions is not a transcendental function?

Which of the following functions is not a transcendental function?
Sin(x)
e^x
log(x)
x^2
7/12

What is the area bounded by the region under the curve y = x^2 from x = 0 to x = 2?

What is the area bounded by the region under the curve y = x^2 from x = 0 to x = 2?
1/3
4/3
16/3
8/3
8/12

What is the second derivative of the function f(x) = 3x^4 - 4x^3 + 2?

What is the second derivative of the function f(x) = 3x^4 - 4x^3 + 2?
12x^3 - 12x^2
12x^3 - 12x^2 + 2
6x^3 - 6x^2
6x^3 - 6x^2 + 2
9/12

What is the limit of (sin x)/x as x approaches 0?

What is the limit of (sin x)/x as x approaches 0?
1
0
undefined
infinity
10/12

What is the area bounded by the region under the curve y = sqrt(x) from x = 0 to x = 4?

What is the area bounded by the region under the curve y = sqrt(x) from x = 0 to x = 4?
4
8
16
2
11/12

What is the derivative of the function f(x) = ln(x^2 + 1)?

What is the derivative of the function f(x) = ln(x^2 + 1)?
(2x)/(x^2 + 1)
(2x^2)/(x^2 + 1)
(2x^3)/(x^2 + 1)
(2x^4)/(x^2 + 1)
12/12

What is the critical point of the function f(x) = 3x^3 - 4x^2 + 2x - 5?

What is the critical point of the function f(x) = 3x^3 - 4x^2 + 2x - 5?
1
2
-2
4/3