If limx- a-fx - gx- - 10 and limx- a fx-2- then find the value of limx- a gx- provided that limx- a fx and limx- a gx exists

If the limits lim_x→ a nbsp;f(x) and nbsp; lim_x→ ag(x) exist, then lim_x→ a [f(x)+g(x)] = lim_x→ a f(x) + lim_x→ a g(x) nbsp; ⇒ 10 = 2+ lim_x→ a g(x) ⇒ ...

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Byju's Answer

Standard XII

Mathematics

Algebra of Limits

If limx→ a[fx...

Question

If $lim x \to a [f (x) + g (x)] = 10$ and $lim x \to a f (x) = 2$ , then find the value of $lim x \to a g (x)$ , provided that $lim x \to a f (x)$ and $lim x \to a g (x)$ exists ___

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Solution

If the limits $lim x \to a f (x)$ and $lim x \to a g (x)$ exist, then $lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$

$\Rightarrow 10 = 2 + lim x \to a g (x)$

$\Rightarrow lim x \to a g (x) = 8$

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If limx→a[f(x)+g(x)]=10 and limx→af(x)=2, then find the value of limx→ag(x), provided that limx→af(x) and limx→ag(x) exists ___

If the limits limx→af(x) and limx→ag(x) exist, then limx→a[f(x)+g(x)]=limx→af(x)+limx→ag(x) ⇒10=2+limx→ag(x) ⇒limx→ag(x)=8

If $lim x \to a [f (x) + g (x)] = 10$ and $lim x \to a f (x) = 2$ , then find the value of $lim x \to a g (x)$ , provided that $lim x \to a f (x)$ and $lim x \to a g (x)$ exists ___

If the limits $lim x \to a f (x)$ and $lim x \to a g (x)$ exist, then $lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$

$\Rightarrow 10 = 2 + lim x \to a g (x)$

$\Rightarrow lim x \to a g (x) = 8$