Question Number 176394 by Matica last updated on 18/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−{cos}\sqrt{\mid{x}\mid}\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{{cosx}}}\:=\:? \\ $$ Commented by cortano1 last updated on 18/Sep/22 $$\:\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{cos}\:\sqrt{\mid\mathrm{x}\mid}\:\right)^{\mathrm{2}} }{\mathrm{1}−\sqrt{\mathrm{cos}\:\mathrm{x}}}\:\left(\mathrm{DNE}\right)…
Question Number 176375 by cortano1 last updated on 17/Sep/22 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{2cos}\:^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{3}}{\mathrm{x}+\sqrt{\mathrm{x}}}\:=?\: \\ $$ Commented by a.lgnaoui last updated on 18/Sep/22 $${posons}\:\:{X}=\frac{\mathrm{1}}{{x}}\:\:\:{x}=\frac{\mathrm{1}}{{X}} \\ $$$$\left[\frac{\mathrm{5}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 110809 by Study last updated on 30/Aug/20 $${li}\underset{{x}\rightarrow\infty} {{m}}\sqrt{{x}!}=? \\ $$ Commented by Her_Majesty last updated on 30/Aug/20 $$\infty \\ $$ Commented by…
Question Number 110760 by bobhans last updated on 30/Aug/20 Answered by john santu last updated on 30/Aug/20 $$\begin{cases}{{x}+\mathrm{1}={m}}\\{{m}\rightarrow\mathrm{0}}\end{cases} \\ $$$${L}=\underset{{m}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2}{m}−\mathrm{tan}\:{m}}{{m}^{\mathrm{3}} } \\ $$$${L}=\:\underset{{m}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:{m}\:\mathrm{cos}\:{m}−\mathrm{tan}\:{m}}{{m}^{\mathrm{3}}…
Question Number 110736 by abdullahquwatan last updated on 30/Aug/20 $$\mathrm{given}\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}\:\mathrm{and}\:{f}\left({x}\right) \\ $$$$\mathrm{is}\:\mathrm{negative}\:\mathrm{on}\:{a}<{x}<{b}.\:\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{\left({x}−{a}\right)^{\mathrm{2}} }{\mathrm{1}−\mathrm{cos}\:\left({f}\left({x}\right)\right)} \\ $$ Commented by abdullahquwatan last updated on…
Question Number 176213 by cortano1 last updated on 15/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{arctan}\:\mathrm{x}}{\mathrm{arcsin}\:\mathrm{x}−\mathrm{x}}\:=? \\ $$ Answered by flamable last updated on 15/Sep/22 $$ \\ $$$${By}\:{the}\:{help}\:{of}\:{Taylor}-{Young}\:{formulae}\:{at}\: \\ $$$${x}\:=\:\mathrm{0}\:{we}\:{have}\:{the}\:{following}\::…
Question Number 176199 by infinityaction last updated on 14/Sep/22 Answered by mr W last updated on 15/Sep/22 $$\left(\mathrm{1}+{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{{k}} ^{{n}} {x}^{{k}} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}}…
Question Number 176154 by cortano1 last updated on 14/Sep/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}\:=? \\ $$ Answered by adhigenz last updated on 14/Sep/22 $$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}^{\mathrm{2}} {x}−\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 176035 by cortano1 last updated on 11/Sep/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:−\mathrm{sin}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{x}} −\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }}\:= \\ $$ Answered by Ar Brandon last updated on 11/Sep/22…
Question Number 175996 by sciencestudent last updated on 10/Sep/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=? \\ $$ Answered by Ar Brandon last updated on 10/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=\underset{{x}\rightarrow\mathrm{0}}…