The value a function approaches as the variable approaches some point. If the function is not continuous, the limit could be different from the value of the function at that point.
What is a limit?
100
Write an equation of the vertical line with x-intercept at 3.
What is X-3=0
100
Find the minimum and maximum values of f(x)=x^2-6x+2
What is x=3
100
Find the indefinite integral 1/2dx
What is 1/2x+c
100
Simplify 5+(-4)/2
What is 1/2
200
A mathematical object that can be interpreted as an area or a generalization of area. Integrals and derivatives are the fundamental objects of calculus.
What is an integral?
200
Find the x and y intercepts of y=x^3-4x
What is y-intercept (0,0) and x-intercept (0,0), (2,0), (-2,0)
200
Find the second derivative of x^2
What is 2
200
Find the indefinite integral 1dx
What is x+c
200
solve for y
5y-12=x
What is y=1/5(x+12)
300
A point at which a function jumps suddenly in value, blows up, or is undefined. The opposite of continuity.
What is discontinuity?
300
Find the x and y intercepts of x=y^2-3
What is x-intercept (-3,0) y-intercept (0, square root of 3) (0, negative square root of 3)
300
Find the differential dy of the function y=x^2
What is 2xdx
300
Find the area bounded by the graphs y=3x^2+1 and y=0 x=0 x=2
What is 10
300
Slope-intercept form
What is y=mx+b
400
The infinitesimal rate of change in a function with respect to one of its parameters. The derivative is one of the key concepts in calculus.
What is a derivative?
400
Differentiate 3x^2 with respect to x
What is 6x
400
Solve the exponential equation e^x=5
What is x=ln5
400
1/(1-2x)^3/2 [negative infinity, 0]
What is 1
400
Point Slope form
What is y-y1=m(x-x1)
500
An integral with upper and lower limits.
What is a definite integral?
500
Differentiate xy^2 with respect to x
What is 2xy dy/dx +y^2
500
Solve the logarithmic equation 3+2lnx=7
What is x=e^2
500
1/cube root of (x-1)dx
What is 3/2
500
Rewrite the expression of the logarithm of a single quantity. (assume x and y are greater than 0)
lnx+2lny