Limits & Continuity
This value is approached by f(x)as x gets close to a number.
What is a limit?
This derivative rule is used for d/dx (x^n) = nx^n-1
What is the power rule?
The derivative represents this on a graph.
What is slope/rate of change?
An integral represents the area _____ a curve.
What is under?
A differential equation contains this type of expression.
What is a derivative?
lim (3x+1)
x->2
What is 7?
Find the derivative of:
f(x) = 3x^2
What is 6x
If f' (x) > 0 the function is doing what?
What is increasing?
Evaluate: ∫ 2x dx
dy/dx = 3
What is y = 3x + C?
A function is continuous if it has no _____ in its graph.
What are breaks/holes/jumps?
This rule is used to differentiate products of functions.
What is the Product Rule?
Critical points occur when f'(x)= 0
What is the derivative is undefined?
This theorem connects derivatives and integrals.
What is the Fundamental Theorem of Calculus?
dy/dx = 2x
What is y = x^2 + C
lim sinx / x
x->0
What is 1?
Find: d/dx (e^x)
This test uses the sign of the second derivative to determine concavity.
What is the Second Derivative Test?
Find the antiderivative:
∫x^2 dx
What is x^3/3 + C?
A series converges if its terms approach this
What is a finite value/limit?
A function is continuous at a point if these three conditions are all met: the limit exists, the function exists, and they are this.
What is equal?
Differentiate:(x^2 + 1)^5
What is 10x(x^2+1)^4?
If f''(x)> 0
What is concave up?
The process of reversing differentiation is called this.
What is antidifferentiation?
This test determines whether an infinite series converges by comparing it to another series.
What is the Comparison Test?