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The function f is given by the formula: f(x)= (4x^3 + 24x^2 + 9x + 54)/(x+6) when x < -6 and by the formula: 4x^2 + 1x + A when -6 <= (greater than or equal) x. What value must be chosen for a in order to make this function continuous at -6?

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Tibor Pejić eNotes educator | Certified Educator

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First you need to find limit of `f(x)` when `x->-6.`

`lim_(x->-6)(4x^3+24x^2+9x+54)/(x+6)=`

Now we divide `4x^3+24x^2+9x+54` by `x-6` so we get

`lim_(x->-6)(4x^2+9)=4(-6)^2+9=153`  

So the limit...

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