Evaluating Limits

Front

What is a limit in calculus?

Back

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

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What does DNE stand for in limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

Front

How do you evaluate the limit of a function as x approaches a specific value?

Back

To evaluate the limit, substitute the value of x into the function, if the function is defined at that point.

Front

What is the limit of a constant function?

Back

The limit of a constant function as x approaches any value is the constant itself.

Front

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

Back

The limit of a polynomial function as x approaches a value is simply the value of the polynomial at that point.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit.

Front

What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?

Back

The limit is 2, found by factoring and simplifying the expression.

Front

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

Back

The limit is 1.

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

Back

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

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What does it mean if a limit approaches infinity?

Back

If a limit approaches infinity, it means the function increases without bound as the input approaches a certain value.