Limx-x3-cosx-x2-sinx2 equal

Lim_x→∞x^3 cosx/x^2+(sinx)^2=lim_x→∞1 cosx/x^3/x^2/x^3+(sinx)^2/x^3 = lim_x→∞1 cosx/x^3/1/x+(sinx)^2/x^3 = 1 0/1/∞+0=1/0 lim_x→∞x^3 cosx/x^2+(sinx)^2=∞ n ...

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Byju's Answer

Standard XI

Mathematics

Standard Limits to Remove Indeterminate Form

limx→∞x3-cosx...

Question

${lim}_{x \to \infty} \frac{x^{3} - c o s x}{x^{2} + (s i n x)^{2}}$ equal

\infty

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Solution

The correct option is A $\infty$
${lim}_{x \to \infty} \frac{x^{3} - c o s x}{x^{2} + (s i n x)^{2}} = {lim}_{x \to \infty} \frac{1 - \frac{c o s x}{x^{3}}}{\frac{x^{2}}{x^{3}} + \frac{(s i n x)^{2}}{x^{3}}}$

$= {lim}_{x \to \infty} \frac{1 - \frac{c o s x}{x^{3}}}{\frac{1}{x} + \frac{(s i n x)^{2}}{x^{3}}}$

= $\frac{1 - 0}{\frac{1}{\infty} + 0} = \frac{1}{0}$

${lim}_{x \to \infty} \frac{x^{3} - c o s x}{x^{2} + (s i n x)^{2}} = \infty$

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limx→∞x3−cosxx2+(sinx)2 equal

The correct option is A ∞limx→∞x3−cosxx2+(sinx)2=limx→∞1−cosxx3x2x3+(sinx)2x3 =limx→∞1−cosxx31x+(sinx)2x3 = 1−01∞+0=10 limx→∞x3−cosxx2+(sinx)2=∞

${lim}_{x \to \infty} \frac{x^{3} - c o s x}{x^{2} + (s i n x)^{2}}$ equal