How Do You Solve the Limit of (x^(1/3) - 4)/(x - 64) as x Approaches 64?

[jog511]

Homework Statement

limx->64 (x^1/3 - 4)/(x - 64)

Homework Equations

The Attempt at a Solution

(64^1/3 -4)/(64 - 64) = 0/0 = not defined

 

[dirk_mec1]

Take the derative of f(x) = x^1/3 -4 at x = 64.

 

[LCKurtz]

Or factor $x-64$ as the difference of two cubes.

 

[jog511]

Thanks. I am trying to help my daughter with AP calculus. The problem states to find the limit algebraically so I cannot take the derivative.

 

[dextercioby]

LC Kurtz gave you the hint: use the decomposition a³-b³

 

[jog511]

We got it. Thanks a lot you guys