- #1

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## Homework Statement

f(x) = [tex]\frac{1-cos(X^2)}{x^3}[/tex]

which identity shoud i use?

and tips on this type of questions? once i can separate them, then i'll be good

thanks!

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- Thread starter myusernameis
- Start date

- #1

- 56

- 0

f(x) = [tex]\frac{1-cos(X^2)}{x^3}[/tex]

which identity shoud i use?

and tips on this type of questions? once i can separate them, then i'll be good

thanks!

- #2

- 1,307

- 109

Do you know a Taylor series for [itex]\cos x[/itex]?

- #3

- 56

- 0

Do you know a Taylor series for [itex]\cos x[/itex]?

yeah, but there's a x^3 on the bottom...

- #4

Cyosis

Homework Helper

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Sure, but the summation isn't over x so you can put the x in the sum or outside the sum.

- #5

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[tex]\frac{1-\sin 2x^3}{x}=\frac{1-\sum_{k=0}^{\infty}\frac{\left( 2x^3\right)^{2k+1}}{(2k+1)!}}{x} = {\scriptstyle \frac{1}{x}}-{\scriptstyle \frac{1}{x}}\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+3}}{(2k+1)!}[/tex]

= {\scriptstyle \frac{1}{x}}-\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+2}}{(2k+1)!}[/tex]

= {\scriptstyle \frac{1}{x}}-\sum_{k=0}^{\infty}\frac{2^{2k-1}x^{6k+2}}{(2k+1)!}[/tex]

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