# Limit calculation

## Homework Statement

Find the limit $$\lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}$$. Needless to say: No L'Hopital's rule, otherwise this thread would not exist.

## The Attempt at a Solution

Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
This is analysis 1 course material .. *blushes*

There is something I have forgotten about, this is supposed to be a really easy problem.
Hints, anyone?

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Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

Find the limit $$\lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}$$. Needless to say: No L'Hopital's rule, otherwise this thread would not exist.

## The Attempt at a Solution

Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
This is analysis 1 course material .. *blushes*

There is something I have forgotten about, this is supposed to be a really easy problem.
Hints, anyone?
Did somebody forbid you from using l'Hospital's rule?

Mark44
Mentor
Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
Of course that won't work -- neither radical contains a square root.

What will work is to multiply each of the numerator and denominator by 1, in a suitable form.

Hint 1: ##(a + b)(a^2 - ab + b^2) = a^3 + b^3##
Hint 2: ##(a + b)(a^4 -a^3b + a^2b^2 - ab^3 + b^4) = a^5 + b^5##

nuuskur and Potatochip911