Find the value of limx-2sin xx

This is a problem where we can use the direct substitution. ⇒lim_x→π/2sin xx= lim_x→π/2sin xlim_x→π/2 x= 1π/2 = 2π We are using the following idea here. If li ...

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Standard XIII

Mathematics

Algebra of Limits

Find the valu...

Question

Find the value of $lim x \to \frac{π}{2} \frac{sin x}{x}$

$0$

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$\frac{π}{2}$

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$\frac{2}{π}$

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limit does not exist

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Solution

The correct option is C
$\frac{2}{π}$

This is a problem where we can use the direct substitution.

$\Rightarrow lim x \to \frac{π}{2} \frac{sin x}{x} = \frac{lim x \to \frac{π}{2} sin x}{lim x \to \frac{π}{2} x} = \frac{1}{\frac{π}{2}}$
$= \frac{2}{π}$

We are using the following idea here.
If $lim x \to a f (x)$ and $lim x \to a g (x)$ exist, then
$lim x \to a \frac{f (x)}{g (x)} = \frac{lim x \to a f (x)}{lim x \to a g (x)}$

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Find the value of limx→π2sinxx

The correct option is C 2π This is a problem where we can use the direct substitution. ⇒limx→π2sinxx=limx→π2sinxlimx→π2x=1π2 =2π We are using the following idea here. If limx→af(x) and limx→ag(x) exist, then limx→af(x)g(x)=limx→af(x)limx→ag(x)

Find the value of $lim x \to \frac{π}{2} \frac{sin x}{x}$