Limits and Continuity

0

Undefined

5

The function has a vertical asymptote at that point

The function is undefined at that point

The function is constant at that point

The left-hand and right-hand limits do not match

0

18

Undefined.

6

$\lim_{x \to \infty} g(x)$

$g(\lim_{x \to \infty})$

$\lim_{g(x) \to \infty} x$

$\lim_{\infty} g(x)$

The behavior of the function as x gets larger and larger

The derivative of the function

The maximum value of the function

The area under the curve of the function

The function is differentiable at that point

The function is decreasing at that point

The function is undefined at that point

The function is continuous at that point

There must be a vertical asymptote at x=a.

The function f(x) approaches a specific value as x approaches a.

The limit as x goes to infinity of f(x) is equal to the limit as x goes to a.

The function has a discontinuity at x=a.

9

0

6

Undefined

The limit does not exist.

-1

1

0

They are not used in calculating vertical asymptotes.

They can exist even if the two-sided limit does not exist.

They always equal each other for continuous functions.

They only exist when there's a discontinuity at that point.