HELP NEEDED. What is the result?

Rotokolo

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Jan 8, 2020
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I’m struggeling, with the result of this limit. Especially “cos(x)^3”. Can someone explain what does it mean? According to my professor it means cos^3(x), she is basically saying that cos(x)^3 = cos^3(x). I don’t think that it’s correct assumption. Can someone explain conventions of using paranthesis in this case. Thank you so much!!

NOTE: I know the calculus, I know how to use powered cos, sin etc. and I know that cos^3(x) is different from cos(x^3).
 

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pka

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Jan 29, 2005
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I’m struggeling, with the result of this limit. Especially “cos(x)^3”. Can someone explain what does it mean? According to my professor it means cos^3(x), she is basically saying that cos(x)^3 = cos^3(x). I don’t think that it’s correct assumption. Can someone explain conventions of using paranthesis in this case.
It is just a difference in notation. \(\displaystyle \sin^4(x)\) is the common notation for the fourth power of the sine function evaluated at \(\displaystyle x\).
However, some authors will write that as \(\displaystyle \sin(x)^4\) or more clearly as \(\displaystyle (\sin(x))^4=[\sin(x)]^4=\{\sin(x)\}^4\). Just a difference in notation.
 

Rotokolo

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Jan 8, 2020
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It is just a difference in notation. \(\displaystyle \sin^4(x)\) is the common notation for the fourth power of the sine function evaluated at \(\displaystyle x\).
However, some authors will write that as \(\displaystyle \sin(x)^4\) or more clearly as \(\displaystyle (\sin(x))^4=[\sin(x)]^4=\{\sin(x)\}^4\). Just a difference in notation.
Thank you so much for your explanation! Appriciate it. You helped a lot
 
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