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Evaluate: lim(x→0) [tanx/x]

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Evaluate: lim(x→0) [tanx/x] 

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When x > 0, tan x > x ⇒ tanx/x > 1

Thus, R.H.L = lim(x→ 0+) [tanx/x] = 1

When x < 0, tan x > x ⇒  tanx/x > 1

Thus, L.H.L = lim(x→ 0–) [tanx/x] = 1

Hence, lim(x → 0) [tanx/x] = 1

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