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Find the limit of $f(x)=\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a-x}-\sqrt{a+x}}$ (at x=0) so that $f(x)$ becomes continuous for all $x$. My answer is $2\sqrt{a}$. Am I right?

Sorry to state the question incorrectly. We have to define $f(x)$ at $x=0$ such that $f(x)$ is continuous for all $x$. In that case my answer is $2\sqrt{a}$.

Let f(x)=$[x]$+$[-x]$ be a function where [.] stands for the greatest integer not greater than x. For any integer $m$, what can we say about $lim_{x \to m}$. Is $f(x)$ contiuous at $x=m$. Sorry for asking such vague question but I am forgetting the exact wording and the options given. This was a question asked in a class test.

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    $f(x) = 0$? $ \ \ $2012-06-24
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    A typo must surely exist in the numerator of this fraction. Do you mean for the middle terms under the radical to have different signs?2012-06-24
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    Oh ... i didn't see that.2012-06-24
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    Echoing others, $f(x) = 0$.2012-06-24
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    @Cocopuffs. How is it $\sqrt{a}$. This is my main problem. Please elaborate.2012-06-24
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    @KunalSuri Each post must contain only one question. Kindly post your second question as a separate post.2012-06-24
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    What is $a$? A positive number?2012-06-24

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