Find the value of lim x -4-sin x-8 x-

We have seen that if lim_x→ a f(x) and lim_x→ a g(x) exists, then lim_x→ a (f(x))^g(x) = [ lim_x→ a f(x) ]^lim_x→ ag(x) In this case, lim_x→π/4 sin x and lim_ ...

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Byju's Answer

Standard XII

Mathematics

Definite Integral as Limit of Sum

Find the valu...

Question

Find the value of $lim x \to \frac{π}{4} [(s i n x)^{\frac{- 8 x}{π}}]$
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Solution

We have seen that if $lim x \to a$ f(x) and $lim x \to a$ g(x)
exists, then

$lim x \to a$ $(f (x))^{g (x)}$ = ${[lim x \to a f (x)]}^{lim x \to a g (x)}$

In this case, $lim x \to \frac{π}{4}$ sin x and $lim x \to \frac{π}{4} \frac{- 8 x}{π}$ exist.

$\Rightarrow lim x \to \frac{π}{4} (s i n x)^{\frac{- 8 x}{π}} = {[lim x \to \frac{π}{4} s i n x]}^{lim x \to \frac{π}{4} \frac{- 8 x}{π}}$

$= {(\frac{1}{\sqrt{2}})}^{- 2}$

$= {(\sqrt{2})}^{2}$

= 2

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Find the value of limx→π4[(sinx)−8xπ] ___

We have seen that if limx→a f(x) and limx→a g(x) exists, then limx→a (f(x))g(x) = [limx→af(x)]limx→ag(x) In this case, limx→π4 sin x and limx→π4−8xπ exist. ⇒limx→π4(sinx)−8xπ=[limx→π4sinx]limx→π4−8xπ =(1√2)−2 =(√2)2 = 2

Find the value of $lim x \to \frac{π}{4} [(s i n x)^{\frac{- 8 x}{π}}]$
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