lim x → 0 sin x − x + x 3 6 x 5 is equal to Options: A . &nbsp 1 120 B . &nbsp 1 160 C . &nbsp 1 2 D . &nbsp 0

Answer: Option A : A lim x → 0 sin x − x + x 3 6 x 5 ....... (1) We know expansion of Sinx. s i n x = x − x 3 3 ! + x 5 5 ! + ........ (2) Substituting (2) in (1) we get l i m x → 0 x 5 5 ! . x 5 = 1 5 ! = 1 120

limx→0sinx−x+x36x5 is equal to

Discussion Forum : Limits Continuity And Differentiability

Question -

$lim x \to 0 \frac{sin x - x + \frac{x^{3}}{6}}{x^{5}}$ is equal to

Options:

A .

\frac{1}{120}

B .

\frac{1}{160}

C .

\frac{1}{2}

D .

0

Answer: Option A
:
A

lim x \to 0 \frac{sin x - x + \frac{x^{3}}{6}}{x^{5}}

....... (1)
We know expansion of Sinx.

s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} +

........ (2)
Substituting (2) in (1) we get

l i m x \to 0 \frac{x^{5}}{5! . x^{5}}

= \frac{1}{5!}

= \frac{1}{120}

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