Trigonometry limit problem

Trigonometry limit problem

Postby Guest » Wed Jan 08, 2020 7:16 pm

I have a problem which needs to be solved without using L'Hosiptal rule.
Can anyone help me?
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Re: Trigonometry limit problem

Postby HallsofIvy » Mon Feb 10, 2020 9:47 pm

The first thing I would do is let [tex]u= \sqrt[3]{cos(x)}[/tex]. Then [tex]cos(x)= u^3[/tex], [tex]cos^2(x)= u^6[/tex], and [tex]sin^2(x)= 1- cos^2(x)= 1- u^6[/tex]. Also, as x goes to 0, cos(x) goes to 1 so u goes to 1.

The problem becomes [tex]\lim_{u\to 1}\frac{u^3- u}{1- u^6}[/tex].

Factor numerator and denominator and cancel where you can.

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