lim-x-0-sin-x-tan-x-x-3-a-1-2-b-1-4-c-1-2-d-1-4-

Question Number 190300 by mnjuly1970 last updated on 31/Mar/23

\lim_{x \to 0} \frac{s i n (x) - t a n (x)}{x^{3}}

a : \frac{1}{2} b : \frac{- 1}{4} c : \frac{- 1}{2} d : \frac{- 1}{4}

Answered by som(math1967) last updated on 31/Mar/23

\underset{x \to 0}{l i m} \frac{s i n x (c o s x - 1)}{x . x^{2} c o s x}

\underset{x \to 0}{l i m} \frac{s i n x}{x} \times \underset{x \to 0}{l i m} \frac{- 2 {s i n}^{2} \frac{x}{2}}{x^{2} c o s x}

\underset{x \to 0}{l i m} \frac{- {s i n}^{2} \frac{x}{2}}{2 \times {(\frac{x}{2})}^{2}} \times \frac{1}{c o s x}

= - \frac{1}{2} (c)

Commented by mnjuly1970 last updated on 31/Mar/23

v e r y n i c e s i r . .

Answered by cortano12 last updated on 31/Mar/23

L = \lim_{x \to 0} \frac{\sin (x) - \tan (x)}{x^{3}}

L = \lim_{x \to 0} \frac{\tan x (\cos x - 1)}{x^{3}}

L = \lim_{x \to 0} \frac{- \sin^{2} x}{x^{2} (\cos x + 1)} = - \frac{1}{2}

Commented by mnjuly1970 last updated on 31/Mar/23

t h x a l o t s i r c o r t a n o