#### gabriel.colon32

##### New member

- Joined
- Oct 31, 2021

- Messages
- 2

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter gabriel.colon32
- Start date

- Joined
- Oct 31, 2021

- Messages
- 2

- Joined
- Dec 30, 2014

- Messages
- 12,215

Just plug in a very large number for x, like 100,000, and evaluate the expression. What you get will be very very close to the exact answer. If you get .50004000567, then the answer will (probably) be 0.5

- Joined
- Oct 31, 2021

- Messages
- 2

Thanks! How did the (1/x) get in the denominator?I'd apply L'Hôpital to the following...

[math]\lim_{x\to \infty} \frac{\sqrt[3]{\left(1-\frac{4}{x}\right)}-1}{\left(\frac{1}{x}\right)} [/math]

- Joined
- Nov 12, 2017

- Messages
- 13,657

Division by 1/x is equivalent to multiplication by ... what?Thanks! How did the (1/x) get in the denominator?

Do you see that Cubist first factored x out of the expression, and then changed that multiplication to a division?

- Joined
- Oct 29, 2019

- Messages
- 1,384

Thanks! How did the (1/x) get in the denominator?

In small steps...

[math] \sqrt[3]{\left(x^3-4x^2\right)}-x[/math][math] = \sqrt[3]{x^3\left(1-\frac{4}{x}\right)}-x[/math][math] = x\left(\sqrt[3]{1-\frac{4}{x}}\right)-x[/math][math] = x\left(\sqrt[3]{\left(1-\frac{4}{x}\right)}-1\right)[/math]

[math] = \frac{x\left(\sqrt[3]{\left(1-\frac{4}{x}\right)}-1\right)}{1}[/math]

divide numerator and denominator by x (which is the same as multiplying both by [imath]\frac{1}{x}[/imath])

[math]=\frac{\sqrt[3]{\left(1-\frac{4}{x}\right)}-1}{\left(\frac{1}{x}\right)} [/math]