Lesson 7: Limits Involving Infinity (worksheet)

Worksheet for Section 2.5 Limits at Infinity Math 1a October 10, 2007 1.

Sketch the graph of a function f that satisfies all of these: • lim f (x) = −∞ x→2

• lim f (x) = ∞ x→∞

•

lim f (x) = 0

x→−∞

• lim+ f (x) = ∞ x→0

• lim− f (x) = −∞ x→0

Find the limits. 2. lim

x→1

2−x (x − 1)2

3. lim− cot x x→π

x3 + 5x x→∞ 2x3 − x2 + 4

4. lim

5.

lim

t→−∞ t3

t2 + 2 + t2 − 1

6. lim

x→∞

p  9x2 + x − 3x

7. lim x − x→∞

√
x

sin2 x x→∞ x2

8. lim

9.

Consider the function

√ f (x) =

2x2 + 1 3x − 5

Sketch the graph (without using your calculator) by finding all its asymptotes and filling it in.