James L.

asked • 01/15/20

What is the limit as x tends to -1 of (X^1/3 + 1)/(1 - x^2/5)

I've just started studying limits using an old textbook. This problem is in the section that introduces limits and before any differentiation rules like L'Hopital's rule so I would like to know how to solve it without using differentiation.

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Patrick B. answered • 01/15/20

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the numerator tends to zero while the denominator tends to 4/5.

quotient tends to zero.


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Mark H.

I read the denominator to be 1 - x^(2/5). I had a real problem evaluating (-1)^(2/5) different calculators give different results. Same issue with (-1)^(1/3). What I think are the correct answers: (-1)^(2/5) = +1, and (-1)^(1/3) = -1 This would mean that top and bottom would both go to zero at x = -1. However, my graphing calculator (desmos) shows that the quotient goes to ~0.83 ???
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01/16/20

James L.

5/6 which is the quotient of the powers 1/3 over 2/5. I just don’t know the algebraic manipulations to get there. I Googled the graph and the limit does look like .83.
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01/16/20

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