Quiz for Limits and Continuity

Q1: limₓ→0 (sin x)/x = ?

A. 0 B. 1 C. ∞ D. Does not exist

Q2: limₓ→0 (1 - cos x)/x² = ?

A. 0 B. 1 C. 1/2 D. ∞

Q3: limₓ→0 (tan x)/x = ?

A. 0 B. 1 C. ∞ D. Undefined

Q4: limₓ→0 (eˣ - 1)/x = ?

A. 0 B. 1 C. e D. Does not exist

Q5: limₓ→∞ (1 + 1/x)^x = ?

A. 0 B. 1 C. e D. ∞

Q6: limₓ→0 (ln(1+x))/x = ?

A. 0 B. 1 C. ∞ D. Does not exist

Q7: limₓ→a (xⁿ - aⁿ)/(x - a) = ?

A. 0 B. n·aⁿ⁻¹ C. n D. Does not exist

Q8: If f(x) = |x|, then f is continuous at x=0?

A. Yes B. No C. Depends on x D. Undefined

Q9: If f(x) = 1/x, is f continuous at x=0?

A. Yes B. No C. Yes, if x≠0 D. Undefined

Q10: limₓ→0 (x·ln x) = ?

A. 0 B. ∞ C. -∞ D. Does not exist

Q11: limₓ→0⁺ (1/x) = ?

A. ∞ B. -∞ C. 0 D. Does not exist

Q12: A function f is continuous if:

A. f is defined at a point B. Limit exists at a point C. Limit equals function value at point D. All of the above

Q13: The left-hand and right-hand limits of a function are equal at x = a. Then the limit exists at x = a?

A. Yes B. No C. Only if function is defined at a D. Only if both are finite

Q14: limₓ→π/2 tan x = ?

A. 0 B. 1 C. ∞ D. Does not exist

Q15: limₓ→0 (aˣ - 1)/x = ?

A. ln a B. a C. 1 D. 0

Q16: Function f(x) = 1 if x ≠ 0 and f(0) = 0. Is f(x) continuous at x=0?

A. Yes B. No C. Yes from left only D. Yes from right only

Q17: If limₓ→a⁻ f(x) ≠ limₓ→a⁺ f(x), function has:

A. Infinite limit B. Discontinuity C. Removable discontinuity D. No discontinuity

Q18: limₓ→0 (1 - cos 2x)/x² = ?

A. 1 B. 2 C. 4 D. Does not exist

Q19: Which of the following is not continuous at x=0?

A. |x| B. sin x C. 1/x D. x²

Q20: limₓ→0 (x⁴ + 2x²)/x² = ?

A. 2 B. x² + 2 C. ∞ D. 0