When a function has no breaks or holes in its graph.

The rule that allows the derivative of x^5 to be 5x^4.

The theorem that states that if f(x) is continuous at every point of [a,b], and F(x) is the anti derivative of f(x) on [a,b], then the integral from a to b of f(x)dx=F(b)-F(a).

The derivative of this is defined as (dy/dt)/(dx/dt).

In this kind of series there is a common ratio and the sum of the terms can be found with the equation
Sn= (a1)/(1-r).

When the answer to a limit is in the form 0/0.

If a function is ___________ then it is also continuous, but if a function is continuous, it is not always ________.

The answer to an integral anytime the upper and lower bound have the same exact value.

Set the y’ coordinate equal to zero when the function has this.

The conditions a function must have in order to use the integral test.

The type of discontinuity when f(x) has a vertical asymptote.

The theorem that states that there must be a value of x on an interval (a,b) where the tangent line is parallel to the line AB.

The formula used to find the length of a curve.

The equation for the second derivative of a parametric equation.

This series test has the following rules and conditions:
an < bn
If series of bn converges, an converges
If series of an diverges, bn diverges

The theorem that states that a function y=f(x) that is continuous on a closed interval [a,b] takes on every value between f(a) and f(b).

The derivative of sec(x).

Find the average value of f(x)=x^2 on [0,4].

sqrt((x’(t))^2 + (y’t)^2)).

This series test can only prove convergence when the limit as n approaches infinity is equal to zero and a(n+1)

lim (3x^2-4x+1)
x->1 (x^2-1)

A method used to different when y is in the equation. Each time a term with y is derived, the term is multiplied by dy/dx.

Evaluate ∫ e^-5x dx from 0 to ∞.

The length of the curve given by equations:
x’(t)= 3cos(t)
y’(t)= -3sin(t)

When using this series test, you will use the limit as n approaches ∞ of the abs.val. of (a(n+1)/an) and the series will only converge if the answer to the limit is <1.