Category: Limits

Question Number 202249 by cortano12 last updated on 23/Dec/23 $$\mathrm{C}=\underset{x\to 0}{\lim }\frac{\mathrm{x}\sqrt[3]{\cos \mathrm{x}}-\sin \mathrm{x}}{{\mathrm{x}}^5}=?$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 202161 by Calculusboy last updated on 22/Dec/23 Answered by som(math1967) last updated on 22/Dec/23 $$\frac{(m+1)!(1+3+5+\dots +2m+3}{2m(m+2)(1+2+3+\dots +m+1)}$$$$=\frac{(m+1)!\frac{m+2}{2}\times 2\{1+(m+2-1)\}}{2m(m+2)\frac{(m+1)(m+2)}{2}}$$$$=\frac{(m+1)!{(m+2)}^2}{m{(m+2)}^2(m+1)}$$$$=\frac{{m}\left({m}+\mathrm{1}\right)×\left({m}−\mathrm{1}\right)!}{{m}\left({m}+\mathrm{1}\right)}…

Question Number 201724 by LimPorly last updated on 11/Dec/23 $$\underset{x\to 0}{\lim }\frac{e^x(x-2)+x+2}{x^3}solveitbynotusing$$$$taylorseriesor{l}^{\prime }hopitalrule.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 201708 by Calculusboy last updated on 10/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 201221 by Calculusboy last updated on 02/Dec/23 Answered by MM42 last updated on 02/Dec/23 $$★★★{tan}^{-1}a-{tan}^{-1}b={tan}^{-1}\left(\frac{a-b}{1+ab}\right)$$$$\Rightarrow{tan}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)−{tan}^{−\mathrm{1}} \left(\frac{{x}}{{x}+\mathrm{2}}\right)={tan}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{2}}{\mathrm{2}{x}^{\mathrm{2}}…