Limits and Continuity
Basics of Derivatives
Basics of Integrals
Applications of Derivatives
Applications of Integrals
100
This calculus term tells us the value that a function approaches as the input approaches some value.
What is a limit?
100
This calculus term tells us the rate of change of a function with respect to a variable.
What is a derivative?
100
This is the area under a function with respect to a variable.
What is integral?
100
This is the derivative of 5x^2
What is 10x?
100
This is is the integral of 3
What is 3x?
200
Determine the limit of the function:
What is 2?
200
This calculus rule is used to find the derivative of a function.
What is the product rule?
200
This is the basic formula for finding the indefinite integral of a single term in a function.
What is (1/n+1)*x^n+1
200
This is the derivative of 7x^4-2x^5?
What is 28x^3-10x^4?
200
This is the integral of 4x
What is 2x^2?
300
Determine which value the function is continuous at: f(x) = (4x + 5) / (9 - 3x)
x = -1
300
Find the derivatives of the following functions: d/dx (sin x), d/dx (cos x)
What is (cos x) and (-sin x)?
300
This is the derivative of (3x+1)*(5x^2-2)
What is (15x^2-6)+(30x^2+10x) (simplified = 45x^2+10x-6)
300
This is the integral of (12x^2)-2
What is 4x^3-2x?
400
What are the 3 conditions of continuity at a point?
The limit must exist at the point
The function must be defined at the point
The limit and the function must have equal values at the point
400
This is the derivative of 6+9x^2/4x-3
What is
400
This is the integral of 28x^3+8x
What is 7x^4+8x?
500
Determine the limit of the function: g(x) = 6/x^2-3x-10
-2 and 5 are Not continuous in this function; so the limits don’t exist.
The function is continuous at 0, so it is a limit.
500
This is the derivative of 9/5x^5+x^3+x^2+3x+C
9x^4+3x^2+2x+3
500
This is the integral of 5x^3-6x+2x+5.
What is the integral of 15x^4-6x^2+2x^2+5x.