For the limit lim x - a fx to exist- fa should be defined

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Byju's Answer

Standard XI

Mathematics

Existence of Limit

For the limit...

Question

For the limit $lim x \to a f (x)$ to exist, f(a) should be defined

True

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False

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Solution

The correct option is B
False

When we find a limit, we don't consider the value of the function at that point. We look for the value of

the function close to the point.

In the above graph, f(x) is not defined. We can still say that the limit exists.

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Similar questions

Write the converse of a conditional statement.

"If Left hand limit = Right hand limit, then we say that limit exists".

(i.e. ${lim}_{x \to a} f (x) = f (a)$ )

Q. For the limit of a function f(x) to exist at a point 'a', need not exist finitely.

$lim x \to a f (x)$ will be closer to $f (a + 2) t h a n f (a + 3)$ .

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

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

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For the limit limx→af(x) to exist, f(a) should be defined

The correct option is B False When we find a limit, we don't consider the value of the function at that point. We look for the value of the function close to the point. In the above graph, f(x) is not defined. We can still say that the limit exists.

For the limit $lim x \to a f (x)$ to exist, f(a) should be defined

The correct option is B
False

When we find a limit, we don't consider the value of the function at that point. We look for the value of

the function close to the point.

In the above graph, f(x) is not defined. We can still say that the limit exists.