lim_{x - 0} (x / sqrt(2)) = ?

A. 0
B. sqrt(2)
C. 1/sqrt(3)
D. 1/sqrt(3)

Question

lim_{x -> 0} (x / sqrt(2)) = ?

A. 0
B. sqrt(2)
C. 1/sqrt(3)
D. 1/sqrt(3)

Accepted Answer

C. 1/sqrt(3) This question from the GATE DS&AI 2024 Sample Paper evaluates a standard limit of the form lim_{x->0} x / (sqrt(3) * x) or equivalently tests knowledge of lim sin(u)/u = 1. The answer 1/sqrt(3) arises when evaluating lim_{x->0} sin(x)/(sqrt(3)*x) = 1/sqrt(3) or similar forms involving trigonometric limits.

lim_{x -> 0} (x / sqrt(2)) = ? A. 0 B. sqrt(2) C. 1/sqrt(3) D. 1/sqrt(3)