Question

Calculus early transcendental functions. Need help with understanding how to get the right answer

Answer 1

Given:

`\lim _(x\to4)(x^3-64)/(x-4)`

solve:

`\begin{gathered} \lim _(x\to4)((x)^3-64)/(x-4) \\ =\lim _(x\to4)((x)^3-(4)^3)/(x-4) \\ =\lim _(x\to4)((x-4)(x^2+4x+4^2))/(x-4) \\ =\lim _(x\to4)(x^2+4x+16) \end{gathered}`
`\begin{gathered} =\lim _(x\to4)(x^2+4x+16) \\ =4^2+4(4)+16 \\ =16+16+16 \\ =48 \end{gathered}`

The value of function is 48 and and extimate limit is 16.