Question Number 44652 by rahul 19 last updated on 02/Oct/18 $${Prove}\:{that}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{ax}\right)^{\frac{\mathrm{1}}{{b}}} −\mathrm{1}}{{x}}\:=\:\frac{{a}}{{b}}. \\ $$ Commented by rahul 19 last updated on 02/Oct/18 $${without}\:{using}\:{L}−{hospital}\:{rule}. \\…
Question Number 110132 by bemath last updated on 27/Aug/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{5cos}\:^{\mathrm{2}} {x}−\mathrm{2cos}\:{x}−\mathrm{3}}{\mathrm{cos}\:{x}−\mathrm{cos}\:\mathrm{3}{x}}\:? \\ $$ Commented by PRITHWISH SEN 2 last updated on 27/Aug/20 $$\mathrm{form}\:\frac{\mathrm{0}}{\mathrm{0}}\:\mathrm{use}\:\mathrm{L}'\mathrm{Hopital} \\…
Question Number 110095 by bemath last updated on 27/Aug/20 $$\:\:\:\left[\frac{{be}}{{math}}\right] \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right) \\ $$ Answered by john santu last updated on 27/Aug/20 $$\:\:\:\:{let}\:\frac{\mathrm{1}}{{x}}\:=\:{h}\:\begin{cases}{{x}\rightarrow\mathrm{0}}\\{{h}\rightarrow\infty}\end{cases}…
Question Number 110086 by john santu last updated on 27/Aug/20 $$\:\:\frac{\spadesuit{JS}\spadesuit}{\bigstar\blacksquare.\bigstar} \\ $$$${If}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\mathrm{2}\mid{ax}\mid−\mathrm{3}{a}^{\mathrm{2}} }{\:\sqrt{{x}}−\sqrt{{a}}\:}\:=\:{P}\:,\:{with}\:{a}>\mathrm{0} \\ $$$${then}\:{the}\:{value}\:{of}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\mathrm{2}{x}^{\mathrm{2}} −\mid{ax}\mid−{a}^{\mathrm{2}} }{{x}−{a}}\:{is} \\ $$$$\_\_\_ \\ $$$$\:\left({a}\right)\:\frac{\mathrm{3}{P}}{\mathrm{4}\sqrt{{a}}}\:\:\:\:\:\:\left({b}\right)\:\frac{\mathrm{3}{P}}{\mathrm{8}\sqrt{{a}}}\:\:\:\:\:\left({c}\right)\:\frac{\mathrm{8}{P}}{\mathrm{3}\sqrt{{a}}}…
Question Number 110075 by bemath last updated on 27/Aug/20 $$\:\:\bigtriangleup\frac{{be}}{{math}}\bigtriangledown \\ $$$$\:\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}.\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} .\mathrm{sin}\:{x}}\:? \\ $$$$\left(\mathrm{2}\right)\:{find}\:\frac{{dy}}{{dx}}\:{from}\:\frac{{x}+{y}}{{x}−{y}}\:=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$ Commented by bobhans last updated on…
Question Number 110072 by bemath last updated on 27/Aug/20 $$\:\:\:\bigtriangleup\frac{{be}}{{math}}\bigtriangledown \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{2}{x}+\mathrm{sin}\:\mathrm{6}{x}+\mathrm{sin}\:\mathrm{10}{x}−\mathrm{sin}\:\mathrm{18}{x}}{\mathrm{3sin}\:{x}−\mathrm{sin}\:\mathrm{3}{x}}=? \\ $$ Answered by john santu last updated on 27/Aug/20 Commented by…
Question Number 175588 by alcohol last updated on 03/Sep/22 Commented by mahdipoor last updated on 04/Oct/22 $$\mathrm{210}=\mathrm{2}×\mathrm{3}×\mathrm{5}×\mathrm{7} \\ $$$${in}\:\mathrm{2022}!=\mathrm{2}^{{a}} ×\mathrm{3}^{{b}} ×\mathrm{5}^{{c}} ×\mathrm{7}^{{d}} ×… \\ $$$${a}\geqslant{b}\geqslant{c}\geqslant{d}\geqslant…\:\Rightarrow…
Question Number 175579 by cortano1 last updated on 03/Sep/22 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{1}−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} .\left(\mathrm{x}^{\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)} −\mathrm{1}\right)}{\mathrm{ln}\:\mathrm{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 44467 by maxmathsup by imad last updated on 29/Sep/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\frac{{x}^{{n}} {sinx}\:−{sin}\left({x}^{{n}} \right)}{{x}}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 30/Sep/18 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 109985 by 150505R last updated on 26/Aug/20 Commented by 150505R last updated on 26/Aug/20 $${please}\:{solve}\:{these}\:{questions}… \\ $$ Commented by Dwaipayan Shikari last updated…