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Author: Tinku Tara

lim-n-n-3-n-n-n-3-n-

Question Number 71777 by Henri Boucatchou last updated on 19/Oct/19 $$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\left(\frac{\boldsymbol{{n}}!\:+\:\mathrm{3}^{\boldsymbol{{n}}} }{\boldsymbol{{n}}^{\boldsymbol{{n}}} \:+\:\mathrm{3}^{\boldsymbol{{n}}} }\right)\:=\:? \\ $$ Commented by mathmax by abdo last updated on…

Question-6238

Question Number 6238 by sanusihammed last updated on 19/Jun/16 Answered by Yozzii last updated on 20/Jun/16 $${Let}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+{n}^{−\mathrm{1}} \right)^{−{n}^{\mathrm{2}} } ={l}. \\ $$$${Let}\:{u}={n}^{−\mathrm{1}} \Rightarrow{l}=\underset{{u}\rightarrow\mathrm{0}^{+} }…

advanced-calculus-prove-that-n-0-1-n-4n-2-1-1-4-2-picsch-pi-2-

Question Number 137307 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:…..{advanced}\:\:\:\:{calculus}….. \\ $$$$\:\:\:\:{prove}\:\:{that}:: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{4}{n}^{\mathrm{2}} +\mathrm{1}}\right)=\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{2}+\pi{csch}\left(\frac{\pi}{\mathrm{2}}\right)\right) \\ $$$$\:\:\:\:\:\:………………………. \\ $$ Answered by Dwaipayan…

show-that-if-f-is-a-differentiable-function-at-the-point-x-a-then-f-is-continuous-at-x-a-

Question Number 71769 by psyche last updated on 19/Oct/19 $${show}\:{that}\:{if}\:{f}\:{is}\:{a}\:{differentiable}\:{function}\:{at}\:{the}\:{point}\:{x}={a},\:{then}\:{f}\:{is}\:{continuous}\:{at}\:{x}={a}. \\ $$ Commented by kaivan.ahmadi last updated on 19/Oct/19 $${if}\:{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)\neq{f}\left({a}\right)\:\Rightarrow{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)−{f}\left({a}\right)\neq\mathrm{0}\Rightarrow \\ $$$${then}\:{f}'\left({a}\right)={lim}_{{x}\rightarrow{a}} \frac{{f}\left({x}\right)−{f}\left({a}\right)}{{x}−{a}}=+\infty\vee−\infty…