Category: Limits

Question Number 35021 by rahul 19 last updated on 14/May/18 $$Findthepointsatwhichthegiven$$$$functionisdiscontinuous:$$$$f\left(x\right)=\mid x\mid sgn(x^3-x).$$ Commented by ajfour last updated on 14/May/18…

Question Number 34982 by rahul 19 last updated on 14/May/18 $$\underset{x\to 1}{\lim }\frac{{nx}^{n+1}-(n+1)x^n+1}{(e^x-e)\sin \pi x}=?$$ Commented by math khazana by abdo last updated…

Question Number 34952 by rahul 19 last updated on 13/May/18 Commented by rahul 19 last updated on 13/May/18 $$a_{n+1}=a_n+\sqrt{1+a_n^2}$$$${and}\:{it}\:{is}\underset{{n}\rightarrow\infty}…

Question Number 34843 by rahul 19 last updated on 11/May/18 $$\underset{x\to \mathrm{\infty }}{{\lim }_{}}\frac{\ln x}{x}=?$$$$Youcanonlyuse$$$$seriesexpansion/sandwichtheorem!$$ Commented by abdo mathsup 649 cc…

Question Number 165868 by cortano1 last updated on 09/Feb/22 $$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\cos \mathrm{x}}{\sin \mathrm{x}-\sqrt[3]{\sin \mathrm{x}+\cos \mathrm{x}}}=?$$ Answered by qaz last updated on 10/Feb/22 $$\underset{\mathrm{x}\to \frac{\pi }{2}}{\lim }\frac{\cos \mathrm{x}}{\sin \mathrm{x}-\sqrt[3]{\sin \mathrm{x}+\cos \mathrm{x}}}$$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}}…