Limits from a Graph

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

What does lim_x→a f(x) represent?

Back

It represents the value that f(x) approaches as x approaches a.

Front

What does it mean if lim_x→c f(x) = L?

Back

It means that as x gets closer to c, the function f(x) gets closer to L.

Front

What is the significance of one-sided limits?

Back

One-sided limits (lim_x→c⁺ and lim_x→c⁻) help determine the behavior of a function as it approaches a point from the right or left.

Front

What does it mean if a limit does not exist (dne)?

Back

It means that the function does not approach a specific value as x approaches a certain point.

Front

How do you find the limit from a graph?

Back

You observe the y-values that the function approaches as x approaches a specific value.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function has a hole at a point, but can be defined at that point to make it continuous.

Front

What is the limit of a constant function?

Back

The limit of a constant function is the constant itself, regardless of the value of x.

Front

What is the limit of a linear function as x approaches a value?

Back

The limit of a linear function is simply the value of the function at that point.

Front

What does it mean if lim_x→a f(x) = f(a)?

Back

It means that the function is continuous at x = a.