Limx- 1 fx-5- and limx- 1 gx - 2 find the value of limx- 1 -gx-fx

If lim_x→ af(x) and lim_x→ ag(x) exists finitely, then lim_x→ a (g(x) nbsp; )^f(x) = [ lim_x→ ag(x) ]^lim_x→ af(x) ⇒lim_x→ 1 ( [g(x)]^f(x) ) = ( lim_x→ 1 ...

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Byju's Answer

Standard XIII

Mathematics

Algebra of Limits

limx→ 1 fx=5,...

Question

$lim x \to 1 f (x) = 5,$ and $lim x \to 1 g (x) = 2$ find the value of $lim x \to 1 ([g (x)]^{f (x)})$ ___

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Solution

If $lim x \to a f (x) and lim x \to a g (x)$ exists finitely, then
$lim x \to a {(g (x))}^{f (x)} = {[lim x \to a g (x)]}^{lim x \to a f (x)}$
$\Rightarrow lim x \to 1 ([g (x)]^{f (x)}) = {(lim x \to 1 g (x))}^{lim x \to 1 f (x)}$
= $2^{5}$
= 32

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limx→1f(x)=5, and limx→1g(x)=2 find the value of limx→1([g(x)]f(x)) ___

If limx→af(x) and limx→ag(x) exists finitely, then limx→a(g(x))f(x)=[limx→ag(x)]limx→af(x) ⇒limx→1([g(x)]f(x))=(limx→1g(x))limx→1f(x) = 25 = 32

$lim x \to 1 f (x) = 5,$ and $lim x \to 1 g (x) = 2$ find the value of $lim x \to 1 ([g (x)]^{f (x)})$ ___

If $lim x \to a f (x) and lim x \to a g (x)$ exists finitely, then
$lim x \to a {(g (x))}^{f (x)} = {[lim x \to a g (x)]}^{lim x \to a f (x)}$
$\Rightarrow lim x \to 1 ([g (x)]^{f (x)}) = {(lim x \to 1 g (x))}^{lim x \to 1 f (x)}$
= $2^{5}$
= 32