Question

Evaluate: lim_(x→0) [sin^–1x/x]

Answer 1

When x > 0, sin^–1x > x ⇒ sin^–1x/x > 1

Thus, R.H.L = lim_{(x→ 0⁺)} [sin–1x/x]= 1

When x < 0, sin^–1 x > x ⇒ sin^–1x/x > 1

Thus, L.H.L = lim_{(x→ 0^–)} [ sin^–1x/x] = 1

Hence, lim _(x→ 0) [ sin^–1x/x] = 1