L'Hopital Problem

Steven G

Elite Member
Joined
Dec 30, 2014
Messages
12,220
It seems that you do not have to know how to do the problem (very unfortunate) but just need the answer.
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
 

Cubist

Senior Member
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]
 
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