2.2b Limit Laws

Front

What is the limit law for 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 evaluated at that point.

Front

Evaluate @@ ext{lim}_{x ightarrow2^+} (2x + 1)@@.

Back

5

Front

Evaluate @@ ext{lim}_{x ightarrow2} (x^2 - 4)@@.

Back

0

Front

What does it mean if @@ ext{lim}_{x ightarrow c} f(x) = L@@?

Back

It means that as x approaches c, the function f(x) approaches the value L.

Front

Evaluate @@ ext{lim}_{x ightarrow3} (x^2 - 9)@@.

Back

0

Front

Back

You may need to apply L'Hôpital's Rule or simplify the expression.

Front

Evaluate @@ ext{lim}_{x ightarrow0} rac{ ext{sin}(x)}{x}@@.

Back

1

Front

Back

It indicates that further analysis is needed, such as factoring or using L'Hôpital's Rule.

Front

Evaluate @@ ext{lim}_{x ightarrow2} (3x^2 + 2x - 8)@@.

Back

6