Question Number 27701 by NECx last updated on 13/Jan/18 $${If}\:{the}\:{function}\:{f}\left({x}\right)\:{satisfies} \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\:\frac{{f}\left({x}\right)−\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}}\:=\pi,\:{evaluate}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right) \\ $$ Commented by abdo imad last updated on 21/Jan/18…
Question Number 27699 by NECx last updated on 13/Jan/18 $${suppose}\:{f}\left({x}\right)=\begin{cases}{{a}+{bx},\:\:{x}<\mathrm{1}}\\{\mathrm{4},\:\:\:\:\:\:\:{x}=\mathrm{1}}\\{{b}−{ax},\:\:{x}>\mathrm{1}}\end{cases}\:{and} \\ $$$${if}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({x}\right)={f}\left(\mathrm{1}\right)\:{what}\:{are}\:{possible} \\ $$$${values}\:{of}\:{a}\:{and}\:{b}? \\ $$$$ \\ $$ Answered by peileng8802 last updated on…
Question Number 27700 by NECx last updated on 13/Jan/18 $${if}\:{f}\left({x}\right)=\begin{cases}{{mx}^{\mathrm{2}} +{n},\:\:\:\:\:{x}<\mathrm{0}}\\{{nx}+{m},\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{{nx}^{\mathrm{3}} +{m},\:\:\:{x}>\mathrm{1}}\end{cases} \\ $$$${for}\:{what}\:{integers}\:{m}\:{and}\:{n}\:{does} \\ $$$${both}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{f}\left({x}\right)\:{and}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)\:{exist}? \\ $$ Commented by NECx last updated…
Question Number 158760 by mathlove last updated on 08/Nov/21 $${f}\left({x}\right)=\left[{sgn}\left({x}^{\mathrm{2}} −\mathrm{1}\right)+{sgn}\left(\mathrm{sin}\:\pi{x}\right)\right] \\ $$$${faind}\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$ Commented by mathlove last updated on 08/Nov/21 $${mister}\:{W}\:{snswer}\:{the}\:{Q} \\…
Question Number 93200 by i jagooll last updated on 11/May/20 Commented by mathmax by abdo last updated on 11/May/20 $${let}\:{f}\left({x}\right)\:=\left(\mathrm{2}^{{x}} \:+\mathrm{3}^{{x}} −\mathrm{12}\right)^{{tan}\left(\frac{\pi{x}}{\mathrm{4}}\right)} \:\Rightarrow{ln}\left({f}\left({x}\right)\right)={tan}\left(\frac{\pi{x}}{\mathrm{4}}\right){ln}\left(\mathrm{2}^{{x}} \:+\mathrm{3}^{{x}} −\mathrm{12}\right)…
Question Number 27663 by abdo imad last updated on 12/Jan/18 $${let}\:{give}\:\:{U}_{{n}} ={n}\:\left(\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:+\:\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} +{n}^{\mathrm{2}} }+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} +{n}^{\mathrm{2}} }\:+….\:\frac{\mathrm{1}}{\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}} }\right) \\ $$$${find}\:{lim}_{{n}−>\propto} \:\:{U}_{{n}} \:\:\:. \\ $$$$…
Question Number 27664 by abdo imad last updated on 12/Jan/18 $${let}\:{give}\:{the}\:{sequence}\:{V}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{k}={n}} \left(\mathrm{1}+\frac{{k}^{\mathrm{2}} }{{n}^{\mathrm{2}} }\:\right)^{\frac{\mathrm{1}}{{n}}} \\ $$$${find}\:{the}\:{value}\:{of}\:{lim}\:_{{n}−>\propto} \:{V}_{{n}} \:\:. \\ $$ Commented by abdo…
Question Number 158735 by Ashraful Islam last updated on 08/Nov/21 Commented by Ashraful Islam last updated on 08/Nov/21 hello , how is it infinity ? anyone can explain please . Commented by mnjuly1970 last updated on…
Question Number 93146 by i jagooll last updated on 11/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\underset{\mathrm{0}} {\overset{\mathrm{x}} {\int}}\left(\mathrm{a}+\mathrm{bcos}\:\mathrm{t}+\mathrm{c}\:\mathrm{cos}\:\left(\mathrm{2t}\right)\right)\mathrm{dt}}{\mathrm{x}^{\mathrm{5}} }\:=\:\mathrm{15} \\ $$ Commented by i jagooll last updated on 11/May/20…
Question Number 27608 by chernoaguero@gmail.com last updated on 10/Jan/18 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ln}\left(\mathrm{x}\:+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right) \\ $$$$\mathrm{plzz}\:\mathrm{help} \\ $$ Commented by abdo imad last…