1. Limits and Continuity

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

limx→1− (1/(x + 1))((x + 6)/x)((3 − x)/7)

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

limh→0− (√6 − √(5h² + 11h + 6))/ h

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

a. limx→1+ (√2x (x − 1)) / |x − 1|

Finding One-Sided Limits Algebraically

Find the limits in Exercises 11–20.

a. limx→0+ (1 − cos x) / |cos x − 1|

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)