Question

Math hw pls help !!

Answer 1

Answer:
`-15x^2+2x-3`

Explanation:

`q(x+h)=-5(x+h)^3 +(x+h)^2 -3(x+h)-3\\\\=-5(x^3 +3x^2 h+3xh^2 +h^3)+(x^2 +2xh+h^2)-3x-3h-3\\\\=-5x^3 -15x^2 h-15xh^2 -5h^3 +x^2+2xh+h^2 -3x-3h-3\\\\`
`q(x+h)-q(x)}=(-5x^3 -15x^2 h-15xh^2 -5h^3 +x^2+2xh+h^2 -3x-3h-3)-(-5x^3 +x^2 -3x-3)}\\\\=-5h^3 -15h^2 x+h^2 -15hx^2 +2hx-3h} \\ \\(q(x+h)-q(x))/(h)=-5h^2 -15hx+h-15x^2 +2x-3\\\\\therefore \lim_(h \to 0) (q(x+h)-q(x))/(h)=\lim_(h \to 0) (-5h^2 -15hx+h-15x^2 +2x-3) \\ \\=\boxed{-15x^2 +2x-3}`