Evaluating the limit $\lim_{x\to0}{\left(\frac{\sqrt[3]{1+cx}}{x}\right)}$

Question

In trying to evaluate the following limit: $$\large\lim_{x\to0}{\left(\frac{\sqrt[3]{1+cx}}{x}\right)}$$

Which gives the indefinite form of:

$$\large\frac{1}{0}$$

What would be the best solution to evaluating this limit?

But is there no way to transform the equation so I get a real number? — Omari Celestine, Aug 18 '17 at 19:13

score 4 · Accepted Answer · answered Aug 18 '17 at 19:07

4

Hint

Look the side limits:

$$\frac{1}{0^+}=\infty$$

$$\frac{1}{0^-}=-\infty$$

answered Aug 18 '17 at 19:07

Arnaldo

Yes but us there no way to transform the equation to I can get an actual value? – Omari Celestine Aug 18 '17 at 19:09
2

I think he's trying to say the limit doesn't exist. – Jirapat Samranvedhya Aug 18 '17 at 19:10
@OmariCelestine: what do you conclude when you get different side limits? – Arnaldo Aug 18 '17 at 19:12
1

That there is no limit. – Omari Celestine Aug 18 '17 at 19:18
@OmariCelestine: correct! – Arnaldo Aug 18 '17 at 19:19

1 Answers1