Evaluate the Limit (just confirmation)

[NATURE.M]

Homework Statement

lim (cubicsquareroot(x) - 2)/(x-8)
x→8

Homework Equations

The Attempt at a Solution

I obtained 1/12 as my final answer, after changing the variable since its in indeterminate form.
..let p=cubicsquareroot(x), then as x→8, p→2
then, p^3=x

Using this logic I obtained 1/12.

Is this correct ?

 

[PrashntS]

Homework Statement

lim (cubicsquareroot(x) - 2)/(x-8)
x→8

Homework Equations

The Attempt at a Solution

I obtained 1/12 as my final answer, after changing the variable since its in indeterminate form.
..let p=cubicsquareroot(x), then as x→8, p→2
then, p^3=x

Using this logic I obtained 1/12.

Is this correct ?

Precisely, Although It'd be nicer if you had done some substitutions.. Yeah is correct!

 

[PrashntS]

Precisely, Although It'd be nicer if you had done some substitutions.. Yeah is correct!

My bad! you have! And when you reach L'Hopital's rule, revisit these questions..

 

[SammyS]

What's a "cubicsquareroot" ?

 

[PrashntS]

What's a "cubicsquareroot" ?

Assumed he meant x^(1/3) *kids today*

 

[NATURE.M]

lol Yeah I mean't x^(1/3). And thanks.

 

[Mark44]

My bad! you have! And when you reach L'Hopital's rule, revisit these questions..

L' Hopital's Rule is not needed in this problem.

The OP apparently revised the original problem to this form:
$$ \lim_{p \to 2} \frac{p - 2}{p^3 - 8}$$

and then factored the denominator to (p - 2)(p² + 2p + 4), and then took the limit.