Limits and Continuity Assessment

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

• 7

• 5

• 8

• 6

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

• 1

• sin(0)

• 1/2

• 0

Determine if the function f(x) = 1/(x-2) is continuous at x = 2.

• The function has a removable discontinuity at x = 2.

• The function is not continuous at x = 2.

• The function is continuous for all x.

• The function is continuous at x = 2.

Evaluate the limit: lim(x→∞) (3x^2 - 5)/(2x^2 + 4).

• 3

• 2

• 4/3

• 3/2

• 1/2

Apply the limit theorem to find: lim(x→1) (x^2 - 1)/(x - 1).

• 3

• 2

• 1

• 0

Analyze the one-sided limit: lim(x→2-) (x^2 - 4)/(x - 2).

• 4

• -4

• 0

• 2

Identify the removable discontinuity of f(x) = (x^2 - 1)/(x - 1).

• x = 0

• x = 1

• x = 2

• x = -1

Evaluate the limit: lim(x→-1) (x^3 + 1)/(x + 1).

• -3

• 3

• 0

• 1

Determine the continuity of f(x) = |x| at x = 0.

• f(x) = |x| is continuous at x = 0.

• f(x) = |x| is undefined at x = 0.

• f(x) = |x| has a jump discontinuity at x = 0.

• f(x) = |x| is discontinuous at x = 0.

Evaluate the limit: lim(x→0) (e^x - 1)/x.

• 0

• 1

• e

• 1/2