Evaluate Limits from graph

Front

What is a limit in calculus?

Back

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

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→a f(x) = L?

Back

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

Front

What is the difference between lim_x→a f(x) and lim_x→a f(x)⁺?

Back

lim_x→a f(x) considers values from both sides, while lim_x→a f(x)⁺ considers values approaching a from the right.

Front

What is the difference between lim_x→a f(x) and lim_x→a f(x)^-?

Back

lim_x→a f(x) considers values from both sides, while lim_x→a f(x)^- considers values approaching a from the left.

Front

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

Back

It means that as x approaches a, the function f(x) increases without bound.

Front

What does it mean if lim_x→a f(x) does not exist (dne)?

Back

It means that f(x) does not approach a specific value as x approaches a.

Front

What is a removable discontinuity?

Back

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

Front

What is a jump discontinuity?

Back

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

Front

How do you evaluate limits graphically?

Back

To evaluate limits graphically, observe the behavior of the function as it approaches the point from both sides.