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Limit calculation

  • Thread starter nuuskur
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  • #1
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Homework Statement


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

Homework Equations




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?
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


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

Homework Equations




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?
 
  • #3
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5,288
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##
 
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