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Homework Statement
evaluate :
[tex] \lim_{x\longrightarrow 0 } \frac{cos(sin\ x) \ - \ cos \ x }{x^4} [/tex]What I've tried
I didnt go for L'Hopitals rule seeing the power of the denominator .
I tried working this one by using the expansion series of sin and cos -:
[tex]
lim= 1-\frac{sin^2x}{2!} + \frac{sin^4x}{4!} \cdots - 1 + \frac{x^2}{2!}- \frac{x^4}{4!} \cdots [/tex]
Dividing by x^4
[tex] = \frac{sin^2x}{x^2}. \frac{-1}{2x^2}+\frac{sin^4x}{24x^4}+\frac{x^2}{2x^4}-\frac{1}{24} [/tex]
[tex] = \frac{1}{2x^2} [/tex]
which gives ∞ as the answer..
Plz suggest a way to work this out
thx
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