Category: Limits

Question Number 153449 by liberty last updated on 07/Sep/21 $$\underset{x\to 0}{\lim }\frac{\sqrt[3]{1+{\tan }^{-1}\left(3x\right)}-\sqrt[3]{1-{\sin }^{-1}\left(3x\right)}}{\sqrt{1-{\sin }^{-1}\left(2x\right)}-\sqrt{1+{\tan }^{-1}\left(2x\right)}}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 153420 by alcohol last updated on 07/Sep/21 $$howmanyx\in \mathbb{R}satisfy{x}^{99}-99x+1=0$$ Answered by mr W last updated on 07/Sep/21 $$f^{\prime }\left(x\right)=99x^{98}-99=0$$$${x}=\pm\mathrm{1}…

Question Number 153352 by liberty last updated on 06/Sep/21 $$\underset{x\to \mathrm{\infty }}{\lim }\sqrt[3]{{27}^x+9^x}-\sqrt{9^x+3^x}=?$$ Answered by MJS_new last updated on 06/Sep/21 $$\underset{{x}\rightarrow+\infty}…

Question Number 153346 by mathlove last updated on 06/Sep/21 Answered by liberty last updated on 06/Sep/21 $$\underset{x\to 2}{\lim }\frac{f\left(x\right)-4}{x-2}=15\to \{\begin{array}{l}f\left(2\right)=4\\ f{}^{\prime }\left(2\right)=15\end{array}$$$$\underset{x\to 2}{\lim }\frac{2x^2-f\left(x\right)}{x-2}=\mathrm{\infty }$$ Answered…

Question Number 87799 by M±th+et£s last updated on 06/Apr/20 $$f\left(x\right)=\{\begin{array}{l}{ax}^2+bx-1⩽x⩽0\\ {cx}^2+d0<x⩽\frac{1}{2}\\ bx+d\frac{1}{2}<x⩽1\end{array}$$$$f\left(x\right)iscontinuouson[-1,1]$$$$proved=0$$$$c=2b$$ Commented by john santu last…