Question Number 184880 by mathlove last updated on 13/Jan/23 $$\underset{{x}\rightarrow\frac{\mathrm{1}}{\pi}} {\mathrm{lim}}\:\:\frac{\pi^{−\mathrm{1}} −{x}}{\frac{\mathrm{1}−\left({x}\pi\right)^{\mathrm{2}} }{\pi^{\mathrm{2}} }}=? \\ $$ Answered by aba last updated on 13/Jan/23 $$\underset{{x}\rightarrow\frac{\mathrm{1}}{\pi}} {\mathrm{lim}}\frac{\pi^{−\mathrm{1}}…
Question Number 184882 by mathlove last updated on 13/Jan/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ln}\left(\mathrm{7}{x}+\mathrm{1}\right)}{{x}}=? \\ $$ Answered by aba last updated on 13/Jan/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{ln}\left(\mathrm{7x}+\mathrm{1}\right)}{\mathrm{x}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}7}\frac{\mathrm{ln}\left(\mathrm{7x}+\mathrm{1}\right)}{\mathrm{7x}}=\mathrm{7} \\ $$…
Question Number 184879 by mathlove last updated on 13/Jan/23 $$\underset{{x}\rightarrow\frac{\mathrm{1}}{\mathrm{4}}} {\mathrm{lim}}\:\mathrm{3}{x}=\frac{\mathrm{3}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$ Answered by aba last updated on 13/Jan/23 $$\mathrm{x}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Terms of…
Question Number 184878 by mathlove last updated on 13/Jan/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ln}\left(\mathrm{1}+{sinx}\right)}{{sinx}}=? \\ $$$${with}\:{out}\:{H}'{L}\:{Roule} \\ $$ Answered by aba last updated on 13/Jan/23 $$\mathrm{let}\:\mathrm{t}=\mathrm{sin}\left(\mathrm{x}\right) \\ $$$$\mathrm{x}\rightarrow\mathrm{0},\:\mathrm{t}\rightarrow\mathrm{0}…
Question Number 184797 by Spillover last updated on 11/Jan/23 $${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\frac{\mathrm{1}}{{x}}} −\mathrm{1}}{{e}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}}\:\:\:{does}\:{not}\:{exist} \\ $$ Commented by MJS_new last updated on 11/Jan/23 $$\mathrm{let}\:{x}=\frac{\mathrm{1}}{{t}}…
Question Number 184796 by Spillover last updated on 11/Jan/23 $${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3}}\mathrm{sin}\:{x}−\mathrm{cos}\:{x}}{{x}−\frac{\pi}{\mathrm{6}}} \\ $$ Commented by MJS_new last updated on 11/Jan/23 $$\mathrm{2} \\ $$…
Question Number 184793 by Spillover last updated on 11/Jan/23 $${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}−\sqrt{{x}+\mathrm{2}}} \\ $$$$ \\ $$ Answered by MJS_new last updated on 11/Jan/23…
Question Number 184798 by Spillover last updated on 11/Jan/23 $${Show}\:{that}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mid{x}\mid}\:\:{does}\:{not}\:{exist} \\ $$ Commented by MJS_new last updated on 11/Jan/23 $${x}\rightarrow\mathrm{0}^{−} :\:\frac{{x}}{\mid{x}\mid}=\frac{{x}}{−{x}}=−\mathrm{1} \\…
Question Number 184795 by Spillover last updated on 11/Jan/23 $${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:}{{x}^{\mathrm{2}} } \\ $$ Commented by MJS_new last updated on 11/Jan/23 $$\frac{\mathrm{3}}{\mathrm{2}} \\…
Question Number 184792 by Spillover last updated on 11/Jan/23 $${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:{x}−\mathrm{sin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}} \\ $$$$ \\ $$ Commented by MJS_new last updated on 11/Jan/23…