If possible, choose k so that the following function is continuous on any interval.
f(x)= (4x^(3)-8x^(2))/(x-2) for x not= 2
k for x=2
alright, i need help on how to start this one, any suggestions would be very helpful, thank you
$\displaystyle \frac{4x^3-8x^2}{x-2} =4x^2 \frac{x-2}{x-2}$
so when $\displaystyle x \ne 2 $:
$\displaystyle \frac{4x^3-8x^2}{x-2} =4x^2$
Hence:
$\displaystyle \lim_{x \to 2} \frac{4x^3-8x^2}{x-2} =4\times 2^2=16$
So if you make $\displaystyle k=16$ then $\displaystyle f$ will be continuous.
RonL