lim as x --> 1 of

(x^(1/3) - 1) / (x^(1/2) - 1)

The answer is supposed to be 2/3.

I tried to use conjugates, but I still end up with a 0 in the denominator.

Could someone work through it? Thanks!

Printable View

- September 19th 2013, 10:31 PMIdentityProblemHelp Finding a Limit
**lim as x --> 1 of**

(x^(1/3) - 1) / (x^(1/2) - 1)

The answer is supposed to be 2/3.

I tried to use conjugates, but I still end up with a 0 in the denominator.

Could someone work through it? Thanks! - September 19th 2013, 10:47 PMibduttRe: Help Finding a Limit
- September 19th 2013, 10:48 PMCesc1Re: Help Finding a Limit
Notice that you can express that as

lim as x--->1 of

f(x)/g(x)

where f(x)= x^(1/3)-1, and g(x)=x^(1/2)-1

Since both limits approach to 0, you can use L'Hopital's rule:

lim as x---> c of

f(x)/g(x)= lim as x-->c of

f'(x)/g'(x) - September 20th 2013, 04:37 PMSorobanRe: Help Finding a Limit
Hello, IdentityProblem!

Quote:

The conjugate of is

The conjugate of is

Now try it again . . .

- September 21st 2013, 02:31 PMIdentityProblemRe: Help Finding a Limit
Thank you, Soroban!

That raises a new question: how do you find a conjugate from scratch? - September 21st 2013, 03:03 PMFelixFelicis28Re: Help Finding a Limit