lim-x-0-x-tanx-sinx-x-

Question Number 138153 by mathlove last updated on 10/Apr/21

\lim_{x \to 0^{+}} \frac{x - ∣ t a n x ∣}{∣ s i n x ∣ - x} = ?

Answered by TheSupreme last updated on 10/Apr/21

f o r x \to 0^{+} ∣ s i n (x) ∣= s i n (x) a n d ∣ t a n (x) ∣= t a n (x)

l i m \frac{x - t a n (x)}{s i n (x) - x} =

f o r x \to 0

t a n (x) \to x + \frac{x^{3}}{3}

s i n (x) \to x - \frac{x^{3}}{6}

l i m \dots . = l i m \frac{- \frac{x^{3}}{3}}{- \frac{x^{3}}{6}} = 2

Commented by greg_ed last updated on 10/Apr/21

cool!

i^{'} ve tried for x \to 0^{-} and the answer is - 1 . :)

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