1. Limits and Continuity

Find the limits in Exercises 49–52. Write ∞ or −∞ where appropriate.

lim x→(−π/2)⁺ sec x

Find the limits in Exercises 49–52. Write ∞ or −∞ where appropriate.

lim θ→0 (2 − cot θ)

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim x/(x² − 1) as

d. x→−1⁻

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x²/2 − 1/x) as

b. x→0⁻

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x²/2 − 1/x) as

d. x→−1

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x² − 1) / (2x + 4) as

b. x→−2⁻

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x² − 3x + 2) / (x³ − 2x²) as

a. x→0⁺

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x² − 3x + 2) / (x³ − 2x²) as

d. x→2

Find the limits in Exercises 53–58. Write ∞ or −∞ where appropriate.

lim (x² − 3x + 2) / (x³ − 4x) as

b. x→−2⁺

Find the limits in Exercises 59–62. Write ∞ or −∞ where appropriate.

lim (2 − 3 / t¹/³) as

a. t → 0⁺

Limits of quotients

Find the limits in Exercises 23–42.

limt→−2 (−2x − 4) / (x³ + 2x²)

Limits of quotients

Find the limits in Exercises 23–42.

limx→1 (x −1) / (√(x + 3) − 2)

Limits with trigonometric functions

Find the limits in Exercises 43–50.

limx→0 (2sin x − 1)

Limits with trigonometric functions

Find the limits in Exercises 43–50.

limx→0 √(7 + sec²x)

Oblique Asymptotes

Graph the rational functions in Exercises 103–108. Include the graphs and equations of the asymptotes.

y = x² / (x − 1)