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Ludmilka [50]
3 years ago
12

Suppose that a function​ f(x) is defined for all real values of x except at xequals=c. can anything be said about the existence

of modifyingbelow lim with x right arrow c f left parenthesis x right parenthesislimx→c f(x)​? give reasons for your answer.
Mathematics
1 answer:
Margaret [11]3 years ago
4 0

we are given that

f(x) is defined for all values of x except at x=c

Limit may or may not exist

case-1:

If there is hole at x=c , then limit exist

case-2:

If there is vertical asymptote at x=c , then limit does not exist

Examples:

case-1:

\lim_{x \to c} \frac{x^2-cx}{(x-c)}

We can simplify it

\lim_{x \to c} \frac{x(x-c)}{(x-c)}

=\lim_{x \to c} x

=c

so, we can see that limit exist and it's value defined

case-2:

\lim_{x \to c} \frac{1}{(x-c)}

Left limit is

\lim_{x \to c-} \frac{1}{(x-c)}

=-\infty

Right Limit is

\lim_{x \to c+} \frac{1}{(x-c)}

=+\infty

so, we can see that left limit is not equal to right limit

so, limit does not exist

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