Evaluating Limits approaching a number

Front

What is the definition of 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 it mean if a limit is DNE (Does Not Exist)?

Back

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

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow 3} (2x + 4)@@

Back

10

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Evaluate the limit: @@ ext{lim}_{x ightarrow 1} (x^2 - 1)@@

Back

0

Front

What is the limit of a constant function as x approaches any number?

Back

The limit is the constant value itself.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow 0} rac{ ext{sin}(x)}{x}@@

Back

1

Front

Back

0

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow 2} (x^2 - 4)@@

Back

0

Front

What is the Squeeze Theorem in relation to limits?

Back

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

Evaluate the limit: @@ ext{lim}_{x ightarrow 2} (x^2 - 2x)@@

Back

0