Question

Give a formula for the extended function that is continuous at the indicated point. f(x)=(x-4)/(sqrt(x)-2), x=4

Answer 1

\(\Large\rm \lim_{x\to 4}\dfrac{x-4}{\sqrt x-2}=f(4)\)

\(\Large\rm =\lim_{x\to 4}\dfrac{(\sqrt x)^2-2^2}{\sqrt x-2}\)

\(\Large\rm =\lim_{x\to 4}\dfrac{[(\sqrt x)-2][\sqrt x)+2]}{\sqrt x-2}\)

\(\Large\rm =\lim_{x\to 4}\sqrt x+2\)

\(\Large\rm =\sqrt 4+2\)

\(\Large\rm =2+2=4\)

\(\Large\rm or\)

\(\Large\rm =-2+2=0\)

\(\Large\rm f(x)=\begin{cases}
\dfrac{x-4}{\sqrt x-2}, x\ne 4\\\\
x=4,~~~~ x=4\\


x=0,~~~~x=4
\end{cases}\)