Warm Up

• Find the derivative of the function: f(x) = -3x2 + 4

• Using the Fundamental Theorem of Calculus and…

• Using the Rules of Derivatives

• Then find the slope at the point (4, -44)

Warm Up #2

• Find the horizontal asymptote of:

3

4

2 6xx 5

5

5 16xx

11.4

Limits at Infinity

Facts About Limits at Infinity• If r is a positive real number, then

• Furthermore, if xr is defined for x < 0, then

• Example: Evaluate

• Does this familiar to you?

1lim 0rx x

1lim 0rx x

4

4

3 5limx

xx

4

5lim 3x x

4

5lim 3 limx x x

3 0 3

Graphical Solution

• Note that the horizontal asymptote is y = 3

Limits at Infinity and Limits of Sequences

Graph We know that the horizontal asymptote is the

line y = 2. Therefore, lim ( ) 2, and lim ( ) 2x x

f x f x

2( )1

xf xx

What happens if the exponents are NOT the same?

3

4

5 71lim

x

xx

3

2

21lim

x

xx

3

4

5limx

xx

3

2

2limx

xx