- #1
adillhoff
- 21
- 0
Homework Statement
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]
Homework Equations
[tex]\lim_{x \rightarrow 4} \frac{4-x}{2-\sqrt{x}}[/tex]
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.