Menu Close

Category: Limits

lim-x-2-11-x-cos-pi-x-2-cot-x-2-

Question Number 193803 by cortano12 last updated on 20/Jun/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{11}−\mathrm{x}}\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{x}−\mathrm{2}}\right)}{\mathrm{cot}\:\left(\mathrm{x}−\mathrm{2}\right)}=? \\ $$ Answered by horsebrand11 last updated on 20/Jun/23 $$\:=\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{3}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\frac{\pi}{\mathrm{x}−\mathrm{2}}\right)}{\mathrm{cot}\:\left(\mathrm{x}−\mathrm{2}\right)} \\ $$$$\:=\:\mathrm{3}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\mathrm{sin}\:\left(\mathrm{x}−\mathrm{2}\right)\:\mathrm{sin}\:\pi\left(\frac{\mathrm{x}−\mathrm{4}}{\mathrm{x}−\mathrm{2}}\right)…

Question-193596

Question Number 193596 by Mingma last updated on 17/Jun/23 Answered by cortano12 last updated on 17/Jun/23 $$\left(\mathrm{1}\right)\:\gamma=\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} −\mathrm{2}\alpha\mathrm{x}−\beta}{\mathrm{2x}}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\:\:\beta=\mathrm{1}\: \\ $$$$\:\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{0}}…

lim-x-2-1-cos-pix-2-x-2-

Question Number 193532 by horsebrand11 last updated on 16/Jun/23 $$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$ Answered by aba last updated on 16/Jun/23 $$\mathrm{let}\:\mathrm{t}=\mathrm{2}−\mathrm{x} \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\pi\mathrm{x}}{\left(\mathrm{2}−\mathrm{x}\right)^{\mathrm{2}}…

Question-193408

Question Number 193408 by cortano12 last updated on 13/Jun/23 $$\:\underline{\underbrace{ }} \\ $$ Answered by MM42 last updated on 13/Jun/23 $${lim}_{{n}\rightarrow\infty} \:\frac{\mathrm{1}}{{n}}×\left(\frac{\mathrm{1}−\left({e}^{\frac{{a}}{{n}}} \right)^{{n}} ×\frac{\mathrm{1}}{{e}^{\frac{{a}}{{n}}} }}{\mathrm{1}−{e}^{\frac{{a}}{{n}}}…

f-x-x-2-x-x-2-1-x-1-2x-1-x-1-thene-find-lim-x-1-f-x-

Question Number 193328 by mustafazaheen last updated on 10/Jun/23 $$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:;\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{1}}\\{\mathrm{2x}+\mathrm{1};\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{1}}\end{cases} \\ $$$$\mathrm{thene}\:\mathrm{find}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$ Answered by cortano12 last updated on 10/Jun/23 $$\:\:\underset{{x}\rightarrow\mathrm{1}}…

Question-193236

Question Number 193236 by Mingma last updated on 08/Jun/23 Answered by MM42 last updated on 09/Jun/23 $${if}\:\:“{p}''\:{is}\:{prime}\:{number}\:\Rightarrow\:\left({p}−\mathrm{1}\right)!\overset{{p}} {\equiv}−\mathrm{1}\:\:\left({wilson}'{d}\:{theorem}\right) \\ $$$${h}=\mathrm{17}{k}+\mathrm{5}\Rightarrow{h}\overset{\mathrm{17}} {\equiv}\:\mathrm{5}\:\: \\ $$ Answered by…

lim-x-0-cosx-1-x-

Question Number 193117 by mustafazaheen last updated on 04/Jun/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$ Answered by Subhi last updated on 04/Jun/23 $${y}\:=\:{lim}_{{x}\rightarrow\mathrm{0}} \:\left({cosx}\right)^{\frac{\mathrm{1}}{{x}}} \\ $$$${ln}\left({y}\right)\:=\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left({cosx}\right)}{{x}}…