Calc. Chapter 2 Review

Front

What is the limit?

Back

The limit is the value that a function approaches as the input approaches a certain point. In this case, the limit is 20.

Front

Which of the following best describes the continuity at x = 0?

Back

Continuous: A function is continuous at a point if the limit as x approaches that point equals the function's value at that point.

Front

Find the vertical asymptote(s) of the function f(x) = (2x)/(x^2 - 1).

Back

The vertical asymptote is x = -2, where the function is undefined.

Front

Consider the function f(x) = (2x)/(x^2 - 1). Prove/disprove continuity at x = -5 using definition notation.

Back

lim f(x) as x→-5 = f(-5): The function is continuous at x = -5.

Front

Find the one-sided limit of f(x) = (2x)/(x^2 - 1) as x approaches 1 from the left.

Back

The one-sided limit exists and is -∞.

Front

Define continuity at a point.

Back

A function is continuous at a point if: 1) f(c) is defined, 2) lim f(x) as x approaches c exists, and 3) lim f(x) as x approaches c = f(c).

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it appropriately.

Front

What is an infinite discontinuity?

Back

An infinite discontinuity occurs when the function approaches infinity or negative infinity as the input approaches a certain value.

Front

What is a jump discontinuity?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point exist but are not equal.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes can be found by setting the denominator of a rational function equal to zero and solving for x.