The Limit of a Function

The idea of approach

Estimating from tables and graphs

One-sided limits

Limits that fail to exist

The function f(x) = (x^2 - 4)/(x - 2) is undefined at x = 2. What is the limit of f(x) as x approaches 2?

A function has left-hand limit 3 and right-hand limit 5 as x approaches 2. What is the two-sided limit at 2?

For f(x) = (sin x)/x near 0, a table gives f(0.1) about 0.9983, f(0.01) about 0.99998, and f(0.001) about 0.9999998, with matching values from the left. What limit do the values suggest?

Which statement correctly distinguishes the two notations lim x to 2 of f equals infinity and lim x to infinity of f equals 2?

Why does the limit of sin(1/x) as x approaches 0 fail to exist?

The function f(x) = 7 takes the value 7 everywhere. What is the limit of f(x) as x approaches any real number a?

The square root function is defined only for x at least 0. What is its right-hand limit as x approaches 0? Answer with a number.

As x approaches 0 from the right, 1/x grows without bound in the positive direction. What symbol describes this limit? Answer with the single word infinity.

The outputs of f(x) = 1/x settle toward a single number as x grows without bound. What is that number? Answer with a number.

A function has left-hand limit 7 and right-hand limit 7 at x = 3. What is its two-sided limit there? Answer with a number.