Compute lim(x→0) sin 3x / x.
A1
B3
C1/3
D0
Answer & Solution
Correct answer: B. 3
Write sin 3x / x = 3 · (sin 3x / 3x), and the bracket tends to 1, giving 3.
Related questions
How many real points of discontinuity does (x + 1)/(x² − 5x + 6) have?Let f(x) = 2x + 1 for x < 2 and x² + 1 for x ≥ 2. What is the limit at x = 2?What does the differentiability of a function at a point guarantee about it there?For f(x) = x³ + x − 1, in which interval must a root lie?How many points in the open interval (0, 3) is ⌊x⌋ discontinuous at?At which of these points is tan x discontinuous?At which real number does f(x) = 1/(x − 3) break down?Define f(x) = (1 − cos x)/x² off zero. Continuity at 0 needs f(0) equal to what?