Lim_x→∞x sinx/x+cosx = lim_x→∞1 sinx/x/1+cosx/x=1 0/1+0=1 [ ∵lim_x→∞sinx/x=lim_x→∞.cosx/x=0 ] ...

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Indeterminate Forms

limx→∞x-sinx/...

Question

${lim}_{x \to \infty} \frac{x - s i n x}{x + c o s x}$ =

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Solution

The correct option is A 1
${lim}_{x \to \infty} \frac{x - s i n x}{x + c o s x} = {lim}_{x \to \infty} \frac{1 - \frac{s i n x}{x}}{1 + \frac{c o s x}{x}} = \frac{1 - 0}{1 + 0} = 1$

$[∵ {lim}_{x \to \infty} \frac{s i n x}{x} = {lim}_{x \to \infty} . \frac{c o s x}{x} = 0]$

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