Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 174863 by cortano1 last updated on 13/Aug/22

Commented by kaivan.ahmadi last updated on 13/Aug/22

$$li\underset{x\to 0}{m}\frac{1-(1+\frac{x^4}{2})(1-\frac{x^4}{2})}{x^8}=$$$$li\underset{x\to 0}{m}\frac{1-(1-\frac{x^8}{4})}{x^8}=\frac{1}{4}$$$$$$$$$$

Commented by cortano1 last updated on 13/Aug/22

$$no$$

Commented by cortano1 last updated on 13/Aug/22

Answered by blackmamba last updated on 13/Aug/22

$$=\underset{x\to 0}{\lim }\frac{1-(1+x^4)\cos {}^2\left(x^2\right)}{2x^8}$$$$=\underset{x\to 0}{\lim }\frac{\sin {}^2\left(x^2\right)-x^4\cos {}^2\left(x^2\right)}{2x^8}$$$$=\underset{x\to 0}{\lim }\frac{(\sin \left(x^2\right)-x^2\cos \left(x^2\right))(\sin \left(x^2\right)+x^2\cos \left(x^2\right))}{2x^8}$$$$=\underset{x\to 0}{\lim }\frac{\sin \left(x^2\right)-x^2\cos \left(x^2\right)}{x^6}$$$$=\underset{x\to 0}{\lim }\frac{\tan \left(x^2\right)-x^2}{{\left(x^2\right)}^3\cos \left(x^2\right)}$$$$=\underset{y\to 0}{\lim }\frac{\tan y-y}{y^3}=\frac{1}{3}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com