Lim x - 0x cos x-sin x-x2-tan x

Lim_x→ 0xcosx+sinx/x^2+tanx Dividing numerator and denominator by x =lim_x→ 0cosx+sinx/x/x+tanx/x =lim_x→ 0cosx+lim_x→ 0sinx/x/lim_x→ 0x+lim_x→ 0tanx/x =1+1/0+1 ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

lim x → 0x co...

Question

${lim}_{x \to 0} \frac{x c o s x + s i n x}{x^{2} + t a n x}$

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Solution

${lim}_{x \to 0} \frac{x c o s x + s i n x}{x^{2} + t a n x}$

Dividing numerator and denominator by x

$= {lim}_{x \to 0} \frac{c o s x + \frac{s i n x}{x}}{x + \frac{t a n x}{x}}$

$= \frac{{lim}_{x \to 0} c o s x + {lim}_{x \to 0} \frac{s i n x}{x}}{{lim}_{x \to 0} x + {lim}_{x \to 0} \frac{t a n x}{x}}$

$= \frac{1 + 1}{0 + 1} = \frac{2}{1} = 2$

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Similar questions

lim x \to 0 \frac{x cos x + 2 sin x}{x^{2} + tan x}

${lim}_{x \to 0} \frac{x c o s x + 2 s i n x}{x^{2} + t a n x}$

You are given
$cos x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .$ ;
$sin x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$ ;
$tan x = x + \frac{x^{3}}{3} + \frac{2 x^{5}}{15} . . . . . .$
Then the value of
$lim x \to 0 \frac{x cos x + sin x}{x^{2} + tan x}$ is

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You are given $c o s x = 1 - \frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \frac{x^{6}}{6!} . . . . . .;$

$s i n x = x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} . . . . . .$

$t a n x = x + \frac{x^{3}}{3} + \frac{2. x^{5}}{15} . . . . . .$

Find the value of $lim x \to 0 \frac{x c o s x + s i n x}{x^{2} + t a n x}$

\lim_{x \to 0} \frac{x \cos x + 2 \sin x}{x^{2} + \tan x}

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limx→0xcosx+sinxx2+tanx

limx→0xcosx+sinxx2+tanx Dividing numerator and denominator by x =limx→0cosx+sinxxx+tanxx =limx→0cosx+limx→0sinxxlimx→0x+limx→0tanxx =1+10+1=21=2

${lim}_{x \to 0} \frac{x c o s x + s i n x}{x^{2} + t a n x}$