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Question Number 125049 by bramlexs22 last updated on 08/Dec/20

$$\underset{x\to 0}{\lim }\frac{{(2+\cos \left(3x\right)-3\cosh \left(x\right))}^4}{\ln (1+x^2)}?$$

Answered by Olaf last updated on 08/Dec/20

$$\underset{x\to 0}{\lim }\frac{{(2+\cos 3x-3\cosh x)}^4}{\ln (1+x^2)}=$$$$\underset{x\to 0}{\lim }\frac{{[2+(1-\frac{9x^2}{2})-3(1+\frac{x^2}{2})]}^4}{x^2-\frac{x^4}{2}+\frac{x^6}{3}-\frac{x^8}{4}}=$$$$\underset{x\to 0}{\lim }\frac{6^4{x}^8}{x^2-\frac{x^4}{2}+\frac{x^6}{3}-\frac{x^8}{4}}=$$$$\underset{x\to 0}{\lim }{6}^4{x}^6=0$$

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