Lim x - 0sin x-x-x3-6 is equal to

The correct option is A x → 0limsin x x+x^3/6 ....... (1) sin x=x x^3/3!+x^5/5! ........ (2) Substituting (2) in (1) we get x→ 0lim x^5/5! =1/5! =1/120 ...

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Byju's Answer

Standard XI

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 0sin ...

Question

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

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Solution

The correct option is A
$lim x \to 0 \frac{sin x - x + x^{3}}{6}$ ....... (1)

$s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!}$ ........ (2)

Substituting (2) in (1) we get

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

$= \frac{1}{5!}$

$= \frac{1}{120}$

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Similar questions

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

is equal to

Q. Find:

lim x \to 0 \frac{sin x - x + \frac{1}{6} x^{3}}{x^{3}} .

Q. Solve:

lim x \to 0 \frac{sin x - x + \frac{1}{6} x^{3}}{x^{5}}

Q. The value of

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

Q. Find c

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

= - \frac{1}{c} .

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limx→0sinx−x+x36 is equal to

The correct option is A limx→0sinx−x+x36 ....... (1) sin x=x−x33!+x55! ........ (2) Substituting (2) in (1) we get limx→0 x55! =15! =1120

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

The correct option is A
$lim x \to 0 \frac{sin x - x + x^{3}}{6}$ ....... (1)

$s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!}$ ........ (2)

Substituting (2) in (1) we get

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

$= \frac{1}{5!}$

$= \frac{1}{120}$