Lim x - 1 fx-5- lim x - 2 gx-6 and lim x - 1 gx-2 find the value of lim x - 1-gx-fx

Lim_x→ af(x) and lim_x→ ag(x) exist, lim_x→ a (f(x) )^g(x) = [ lim_x→ af(x) ]^lim_x→ ag(x) ⇒lim_x→ 1 ( [g(x)]^f(x) ) = ( lim_x→ 1g(x) )^lim_x→ 1f(x) = 2^5 ...

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Byju's Answer

Standard XI

Mathematics

Algebra of Limits

lim x → 1 fx=...

Question

$lim x \to 1 f (x) = 5$ , $lim x \to 2 g (x) = 6$ 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

$lim x \to a f (x) a n d lim x \to a g (x) e x i s t,$
$lim x \to a {(f (x))}^{g (x)} = {[lim x \to a f (x)]}^{lim x \to a g (x)}$
$\Rightarrow lim x \to 1 ([g (x)]^{f (x)}) = {(lim x \to 1 g (x))}^{lim x \to 1 f (x)}$
= $2^{5}$
= 32

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limx→1f(x)=5, limx→2g(x)=6 and limx→1g(x)=2 find the value of limx→1 ([g(x)]f(x))

limx→af(x)andlimx→ag(x)exist, limx→a(f(x))g(x)=[limx→af(x)]limx→ag(x) ⇒limx→1([g(x)]f(x))=(limx→1g(x))limx→1f(x) = 25 = 32

$lim x \to 1 f (x) = 5$ , $lim x \to 2 g (x) = 6$ and $lim x \to 1 g (x) = 2$ find the value of $lim x \to 1$ $([g (x)]^{f (x)})$

$lim x \to a f (x) a n d lim x \to a g (x) e x i s t,$
$lim x \to a {(f (x))}^{g (x)} = {[lim x \to a f (x)]}^{lim x \to a g (x)}$
$\Rightarrow lim x \to 1 ([g (x)]^{f (x)}) = {(lim x \to 1 g (x))}^{lim x \to 1 f (x)}$
= $2^{5}$
= 32