Posted by **Unknown** on Friday, May 3, 2013 at 9:17pm.

The function f is given by the formula f(x)=6x^3+17x^2+4x+21/x+3

when x<–3 and by the formula

f(x)=2x^2–4x+a

What value must be chosen for a in order to make this function continuous at -3?

- calculus -
**Reiny**, Friday, May 3, 2013 at 10:51pm
mmmh, took me a while to understand what the question is asking.

First of all you will need brackets:

f(x) = (6x^3+17x^2+4x+21)/(x+3)

= (6x^2 - x + 7) , where x≠ -3

= (x+1)(6x-7)

we want this to be the same as

2x^2 - 4x + a

If 6x^2 - x + 7 = 2x^2 - 4x + a

4x^2 + 3x + 7 = a

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