(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Define the function at a so as to make it continuous at a.

[tex]f(x)=\frac{4-x}{2-\sqrt{x}}; a = 4[/tex]

2. Relevant equations

[tex]\lim_{x \rightarrow 4} \frac{4-x}{2-\sqrt{x}}[/tex]

3. The attempt at a solution

I cannot think of how to manipulate the denominator to achieve f(4), so I start by finding the left and right hand limits then applying the informal definition of a limit.

[tex]\lim_{x \rightarrow +4}\frac{4-x}{2-\sqrt{x}} = 4[/tex]

[tex]\lim_{x \rightarrow -4}\frac{4-x}{2-\sqrt{x}} = 4[/tex]

I do not know if this is the right way to solve this problem though. If I use this method, I am still left with a function where f(4) is discontinuous. Any hints would be greatly appreciated.

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# Homework Help: Limits and Continuous Functions problem

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