Limits

Front

What is a limit in calculus?

Back

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

Front

How do you denote the limit of a function f(x) as x approaches a?

Back

It is denoted as lim (x -> a) f(x).

Front

What is the limit of a constant function?

Back

The limit of a constant function is the constant itself.

Front

What is the limit of f(x) as x approaches infinity for a rational function?

Back

It depends on the degrees of the numerator and denominator.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) is squeezed between g(x) and h(x) and both g(x) and h(x) approach L as x approaches a, then f(x) also approaches L.

Front

What is the limit of sin(x)/x as x approaches 0?

Back

The limit is 1.

Front

What is the difference between one-sided limits and two-sided limits?

Back

One-sided limits consider the approach from one direction (left or right), while two-sided limits consider both directions.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms by differentiating the numerator and denominator.

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 at that point.

Front

What is the limit of (1/x) as x approaches 0 from the right?

Back

The limit is positive infinity.