Limx- a-fx-gx- - limx- a fx - limx- a gxis valid if limx- afx does not exists-

The result lim_x→ a[f(x)+g(x)] = lim_x→ a f(x) + lim_x→ a g(x) is true only when lim_x→ a nbsp;f(x) and nbsp;lim_x→ a g(x) exists. It has been given that ...

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Byju's Answer

Standard XIII

Mathematics

Algebra of Limits

limx→ a[fx+gx...

Question

$lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$
is valid if $lim x \to a f (x)$ does not exists?

True

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False

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Solution

The correct option is B
False

The result $lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$ is true only when $lim x \to a f (x)$ and $lim x \to a g (x)$ exists.

It has been given that $lim x \to a f (x)$ does not exists, so the above equation is not valid.

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Similar questions

Q. limx→a [f(x)+g(x)]=10 and limx→a f(x)=2. Then, limx→ag(x), if it exists, is

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 both $lim x \to a f (x)$ and $lim x \to a g (x)$ and exist finitely and $lim x \to a g (x) = 0$ , then
$lim x \to a \frac{f (x)}{g (x)} = \frac{lim x \to a f (x)}{lim x \to a g (x)}$

Q. If

lim x \to a {\frac{f (x)}{g (x)}}

exists, then

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limx→a[f(x)+g(x)]=limx→af(x)+limx→ag(x) is valid if limx→af(x) does not exists?

The correct option is B False The result limx→a[f(x)+g(x)]=limx→af(x)+limx→ag(x) is true only when limx→af(x) and limx→ag(x) exists. It has been given that limx→af(x) does not exists, so the above equation is not valid.

$lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$
is valid if $lim x \to a f (x)$ does not exists?

The correct option is B
False

The result $lim x \to a [f (x) + g (x)] = lim x \to a f (x) + lim x \to a g (x)$ is true only when $lim x \to a f (x)$ and $lim x \to a g (x)$ exists.

It has been given that $lim x \to a f (x)$ does not exists, so the above equation is not valid.