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!

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- Aug 9th 2009, 07:20 AMlive_laugh_luv27continuous function
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! - Aug 9th 2009, 07:50 AMPlato
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 $\displaystyle a=\frac{-1}{4}$