Question

#62 please! Will need some steps.

Answer 1

The limit is 3x²

Explanation:

Recall the definition of a derivative is
`\displaystyle f'(x) = \lim_(h \to 0) (f(x+h)-f(x))/(h)` where
`\Delta x=h`:

`\displaystyle f'(x) = \lim_(h \to 0) (f(x+h)-f(x))/(h)\\\\f'(x) = \lim_(h \to 0) ((x+h)^3-x^3)/(h)\\\\f'(x) = \lim_(h \to 0) (x^3+3xh^2+3x^2h+h^2-x^3)/(h)\\\\f'(x) = \lim_(h \to 0) (3xh^2+3x^2h+h^2)/(h)\\\\f'(x) = \lim_(h \to 0) 3xh+3x^2+h\\\\f'(x) = 3x(0)+3x^2+0\\\\f'(x) = 3x^2`