Is the statement "if limit of f(x)=L as x approaches c, then f(c)=L" a true or false statement?

Answer 1

It's a false statement.

First we have to suppose that #L# is finite, Then #f(x)# may not even be defined for #x=c# as in the case:
#lim_(x->0) sinx/x = 1#

In fact the property:

#lim_(x->c) f(x) = f(c)#
is what defines a function that is continuous in #x=c#.
In other words the statement is equivalent to saying that #f(x)# is continuous in #x=c# and not all functions are continuous in their entire domain.
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Answer 2
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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