SOLUTION: what's the limit:
lim f(x){{{ (square root of x-2)/((x^2)-4)}}} as x approaches 2 from the right
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Question 207395: what's the limit:
lim f(x) as x approaches 2 from the right
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
)
Since both numerator and denominator go to zero as 
approaches 2 from the right, you need to use L'Hôpital's Rule.
If \ =\ \lim_{x\rightarrow c}g(x)\ =\ 0)
or 
and if /g'(x))
exists, then
}{g(x)}\ =\ \lim_{x\rightarrow c}\frac{f'(x)}{g'(x))
The rule also applies to one-sided limits, so:
If \ =\ \lim_{x\rightarrow c^\pm}g(x)\ =\ 0)
or and if /g'(x))
exists, then
}{g(x)}\ =\ \lim_{x\rightarrow c^\pm}\frac{f'(x)}{g'(x))
So take the first derivative of each of the numerator and denominator functions.
\ =\ \lim_{x\rightarrow 2^+}\left(\frac{\frac{1}{2\sqrt{x-2}}}{2x}\right)\ =\ +\infty)
John
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