Mastering Limits in Calculus

Evaluate the limit: lim (x→3) (2x + 1).

• 7

• 8

• 9

• 6

Calculate the one-sided limit: lim (x→2⁻) (x² - 4)/(x - 2).

• 2

• 0

• 4

• -4

Determine if the function f(x) = 1/(x - 1) is continuous at x = 1.

• The function is continuous at x = 1.

• The function is continuous everywhere.

• The function has a removable discontinuity at x = 1.

• The function is not continuous at x = 1.

Analyze the limit at infinity: lim (x→∞) (3x² - 5)/(2x² + 4).

• 3/2

• 4/3

• 2

• 1/2

Evaluate the limit: lim (x→0) (sin(5x)/x).

• 0

• 5

• 10

• 1

Calculate the one-sided limit: lim (x→0⁺) (1/x).

• ∞

• 0

• -∞

• 1

Determine if the function f(x) = √(x) is continuous at x = 0.

• Yes, f(x) = √(x) is continuous at x = 0.

• No, f(x) = √(x) has a jump discontinuity at x = 0.

• No, f(x) = √(x) is not defined at x = 0.

• Yes, f(x) = √(x) is discontinuous at x = 0.

Analyze the limit at infinity: lim (x→-∞) (4x + 1)/(2x - 3).

• 0

• 2

• 1/2

• -2

Evaluate the limit: lim (x→1) (x³ - 1)/(x - 1).

• 2

• 4

• 3

• 1

Calculate the one-sided limit: lim (x→-1⁻) (x² + 1)/(x + 1).

• 0

• 1

• -∞

• ∞