Question Number 73569 by Rio Michael last updated on 13/Nov/19 $${let}\:{f}\left({x}\right)\:=\:\frac{{tanx}}{{tan}\mathrm{2}{x}}\:.\:{Find}\:{the}\:{points}\:{of}\:{discontinuity} \\ $$$${of}\:{f}\:{on}\:\left[\mathrm{0},\mathrm{2}\pi\right]\:{and}\:{determine}\:{wether}\:{each}\:{duscontinuity}\:{is} \\ $$$${a}\:{point}\:{discontinuity},{a}\:{jump}\:{discontinuity},{or}\:{a}\:{vertical}\:{asymtote} \\ $$$$ \\ $$ Commented by Rio Michael last updated…
Question Number 8032 by Nayon last updated on 28/Sep/16 $${find}\:{the}\:{real}\:{root}: \\ $$$$\mathrm{99}{x}^{\mathrm{3}} +\mathrm{297}{x}^{\mathrm{2}} +\mathrm{594}{x}−\mathrm{7867}=\mathrm{0} \\ $$ Answered by prakash jain last updated on 28/Sep/16 $${x}={y}−\mathrm{1}…
Question Number 139101 by mnjuly1970 last updated on 22/Apr/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:…….{nice}\:\:\:{calculus}….. \\ $$$$\boldsymbol{\phi}\overset{???} {=}\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\mathrm{1}−{xy}}\left(−{ln}\left({xy}\right)\right)^{\mathrm{2019}} {dxdy} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:……… \\ $$ Answered by Dwaipayan…
Question Number 73566 by Rio Michael last updated on 13/Nov/19 $${show}\:{that}\:{f}\left({x}\right)\:=\:\mid{x}\mid\:{is}\:{not}\:{differentiable}\:{at}\:{x}=\mathrm{0},\:{where}\:\mid{x}\mid \\ $$$${denotes}\:{he}\:{absolute}\:{value}\:{function} \\ $$ Commented by Rio Michael last updated on 13/Nov/19 $${thanks}\:{sir}, \\…
Question Number 8031 by Nayon last updated on 28/Sep/16 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{2}}\:\approx\frac{\mathrm{19601}}{\mathrm{13860}} \\ $$ Answered by prakash jain last updated on 28/Sep/16 $$\sqrt{\mathrm{2}}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{2}}}\:\:\:\:…\left({i}\right) \\ $$$$\mathrm{putting}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{2}}\:\mathrm{from}\:\left({i}\right)\:\mathrm{in}\:\mathrm{RHS} \\ $$$$\mathrm{of}\:\left({i}\right)…
Question Number 73567 by Rio Michael last updated on 13/Nov/19 $${Determine}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:{fir}\:{which}\:{the}\:{function}\:{f},{defined}\:{by} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{−\mathrm{2}{sinx},\:\:{x}\:<\:−\frac{\pi}{\mathrm{2}}}\\{{asinx}\:+\:{b},−\frac{\pi}{\mathrm{2}}\:\leqslant\:{x}\:<\:\frac{\pi}{\mathrm{2}}}\\{{cosx},\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:>\:\frac{\pi}{\mathrm{2}}}\end{cases} \\ $$$${is}\:{continouos} \\ $$ Commented by Rio Michael last updated on 13/Nov/19…
Question Number 139103 by ajfour last updated on 22/Apr/21 $${x}^{\mathrm{3}} −{x}={c}\:\:\:;\:\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\:.\:{Find}\:{x}. \\ $$ Commented by ajfour last updated on 24/Apr/21 Answered by mr W last…
Question Number 73565 by Rio Michael last updated on 13/Nov/19 $${investigate}\:{the}\:{continuity}\:{of}\:{f}\:,{given}\:{by} \\ $$$${f}:\:{x}\:\rightarrow\:\begin{cases}{\mathrm{1}−{x},\:{if}\:{x}<\mathrm{1}}\\{\mathrm{0},{if}\:{x}\:=\mathrm{1}}\\{{x}^{\mathrm{2}} −\mathrm{3}{x}\:+\:\mathrm{2},{if}\:{x}\:>\mathrm{1}}\end{cases} \\ $$$${at}\:{the}\:{point}\:{x}\:=\mathrm{1} \\ $$$$ \\ $$ Commented by Rio Michael last…
Question Number 8027 by Nayon last updated on 28/Sep/16 $${prove}\rightarrow\:{any}\:{prime}\:{number}>\mathrm{2}\: \\ $$$${can}\:{be}\:{written}\:{into}\left(\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}\:} \right)\:{where} \\ $$$$\left({x},{y}\right)\in{N} \\ $$ Commented by FilupSmith last updated on 28/Sep/16…
Question Number 8026 by Nayon last updated on 28/Sep/16 $${Find}\:{the}\:{factor}\:{of}\:\left(\mathrm{3}^{\mathrm{200}} +\mathrm{4}\right) \\ $$ Answered by Rasheed Soomro last updated on 28/Sep/16 $$\mathrm{3}^{\mathrm{200}} +\mathrm{4} \\ $$$$=\left(\mathrm{3}^{\mathrm{100}}…