This limits problem doesn't seem to have a "correct" answer?

Asked Apr 01 '20 at 16:18

Active Apr 01 '20 at 16:22

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$$\lim\limits_{x\to 0}\left(\dfrac{(x+3x^2)^{1/3}-x^{1/3}}{x^{1/3}}\right)$$

I was able to evaluate the answer to be 0, by splitting the denominator for the both the numerators, and simplifying the term within the bracket and the term at the end separately - and simply substituting 0 in the end. However, the answer, apparently, is 1. Would appreciate a solution or any explanation :)

edited Apr 01 '20 at 16:22

JMoravitz

79,518

asked Apr 01 '20 at 16:18

NitinReddy

2

Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. For equations, please refer to this MathJax tutorial. – Pantelis Sopasakis Apr 01 '20 at 16:21
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The correct answer is $0$, as you say. – TonyK Apr 01 '20 at 16:23
@TonyK Really? I mean I'm not exactly the best at math, and the source of this question (and the answer) is pretty reputed, so I doubted myself. Anyway, thanks! – NitinReddy Apr 01 '20 at 16:26
3

Write it as $\lim_{x\to 0} \left( (1 + 3 x)^{1/3} - 1 \right)$ and it's obvious. – Robert Israel Apr 01 '20 at 16:27
@RobertIsrael Yep, that was my approach. Thank you! – NitinReddy Apr 01 '20 at 16:28
It is of course 0 as you done it well @NitinReddy. – EDX Apr 01 '20 at 16:28
If you changed the denominator to $x^{4/3}$ then you would get a limit of $1$ as $x \to 0$ – Henry Apr 01 '20 at 16:32

This limits problem doesn't seem to have a "correct" answer?

0 Answers0