Find a value for a so that the function
$\displaystyle f(x) = \{2x-5, x<2 $
$\displaystyle ax^2, x\ge2$
is continuous. I came up with the answer -1/4, but not sure how, or if it is correct.
Thanks!
If x is near 2 but less than 2, $\displaystyle x \approx 2\;\& \,x < 2$, then $\displaystyle 2x - 5 \approx - 1$.
If x is near 2 but greater than 2, $\displaystyle x \approx 2\;\& \,x > 2$, then we must have $\displaystyle ax^2 \approx - 1$. Therefore $\displaystyle a=\frac{-1}{4}$