Question

compute the limit
lim (8x-x^2+3)^3 as x goes to 2

Answer 1

\[\lim_{x\to2}(-x^2+8x+3)^3=(-(2)^2+8(2)+3)^3=?\]

Answer 2

OK SO I JUST SOLVE RIGHT?

Answer 3

Yes

Answer 4

However, when you start seeing things like\[\lim_{x\to2}\frac{x^2+3x+2}{x-2},\]then you have to do some algebraic manipulation.

Answer 5

OK. FOR THE EQUATION ABOVE WOULD IT (-(4)+16+9 ?

Answer 6

Where did you get that \(9\) from?

Answer 7

I got it from the last part of the equation where it says 3)^3. Or did I do that wrong

Answer 8

yes, that's wrong
^3 is the last step; do what's in the parentheses first

Answer 9

and ^3 does not mean times 3, it means to the third power

Answer 10

so would it be (-4+16+3)^3

Answer 11

Yes. What does that evaluate to?

Answer 12

-4+16+3= 15 so then I do 15^3 Right? so that would equal 3375

Answer 13

That's right.

Answer 14

Thank you for your help