Question Number 162189 by SANOGO last updated on 27/Dec/21 $${show}\:{the}\:{converge}^{} {nce}\:{and}\:{calculate} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}}\:{dt} \\ $$ Commented by Ar Brandon last updated on 27/Dec/21…
Question Number 162190 by naka3546 last updated on 27/Dec/21 $$\lfloor\:\frac{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2}} −\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{3}} +\mathrm{1}}{\mathrm{3}^{\mathrm{3}} −\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{4}} +\mathrm{1}}{\mathrm{3}^{\mathrm{4}} −\mathrm{1}}\:+\:\ldots+\:\frac{\mathrm{3}^{\mathrm{2017}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2017}} −\mathrm{1}}\:\rfloor\:=\:\:? \\ $$ Answered by mr W last…
Question Number 31109 by naka3546 last updated on 02/Mar/18 $$\boldsymbol{{a}}^{\mathrm{4}} \:+\:\boldsymbol{{b}}^{\mathrm{4}} \:+\:\mathrm{13}\:\:\:{is}\:\:{a}\:\:{possible}\:\:{largest}\:\:{prime}\:\:{number}\:. \\ $$$$\boldsymbol{{a}}\:\:{and}\:\:\boldsymbol{{b}}\:\:{are}\:\:{prime}\:\:{numbers}\:. \\ $$$${Find}\:\:\boldsymbol{{a}}\:\:{and}\:\:\boldsymbol{{b}}\:. \\ $$ Commented by rahul 19 last updated on…
Question Number 96616 by mathocean1 last updated on 03/Jun/20 Answered by Rio Michael last updated on 03/Jun/20 $${A}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{and}\:{B}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix} \\ $$$${AB}\:=\:\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{ax}\:+\:{by}}\\{{bx}\:+\:{cy}}\end{pmatrix} \\ $$$${BA}\:=\:\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\begin{pmatrix}{{a}}&{{b}}\\{{b}}&{{c}}\end{pmatrix}\:\mathrm{impossible}\:\mathrm{since}\: \\ $$$$\mathrm{order}\:\left(\mathrm{A}\right)\:=\:\mathrm{2}\:×\mathrm{2}\:\:\mathrm{and}\:\mathrm{order}\:\left(\mathrm{B}\right)\:=\:\mathrm{2}×\:\mathrm{1} \\…
Question Number 96617 by mathocean1 last updated on 03/Jun/20 $${Given}\:{matrix}\:{A}\begin{bmatrix}{{a}\:\:\:\:\:{c}}\\{{b}\:\:\:\:\:{d}}\end{bmatrix}{and}\:{B}\begin{pmatrix}{{x}}\\{{y}_{} }\end{pmatrix}. \\ $$$${Determinate}\:{A}×{B}\:{and}\:{B}×{A}. \\ $$ Commented by bobhans last updated on 03/Jun/20 $$\mathrm{B}×\mathrm{A}\:\mathrm{undefine} \\ $$…
Question Number 96606 by Hamida last updated on 03/Jun/20 Commented by Tony Lin last updated on 03/Jun/20 $${y}'=\frac{\mathrm{5}}{\mathrm{13}}{e}^{\frac{\mathrm{5}}{\mathrm{13}}{x}} +\mathrm{13}{sec}\left(\mathrm{13}{x}\right){tan}\left(\mathrm{13}{x}\right) \\ $$ Terms of Service Privacy…
Question Number 162139 by LEKOUMA last updated on 27/Dec/21 Answered by alephzero last updated on 27/Dec/21 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\sqrt{{x}}}{\mathrm{1}−\mathrm{ln}\:\left({e}−{x}\right)}\:=\: \\ $$$$=\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\frac{{d}}{{dx}}\left(\sqrt{{x}}\right)}{\frac{{d}}{{dx}}\left(\mathrm{1}−\mathrm{ln}\:\left({e}−{x}\right)\right)}\:=\: \\ $$$$=\underset{{x}\rightarrow\mathrm{0}^{+}…
Question Number 96600 by Hamida last updated on 03/Jun/20 Answered by Rio Michael last updated on 03/Jun/20 $$\:{y}\:=\:\frac{\mathrm{4}}{\mathrm{7}}{x}^{\mathrm{3}} \:−\:\frac{\mathrm{2}}{\mathrm{3}}{x}^{−\mathrm{1}} \\ $$$${y}\:'\:=\:\frac{\mathrm{12}}{\mathrm{7}}{x}^{\mathrm{3}} \:+\:\frac{\mathrm{2}}{\mathrm{3}{x}^{\mathrm{2}} }\: \\ $$$${y}'\mid_{{x}=\mathrm{7}}…
Question Number 96586 by M±th+et+s last updated on 02/Jun/20 $${find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)={x}^{{x}} \\ $$$${for}\:{x}\in\mathbb{R}^{+} \\ $$ Answered by 1549442205 last updated on 02/Jun/20 $$\mathrm{y}=\mathrm{x}^{\mathrm{x}} \Rightarrow\mathrm{lny}=\mathrm{xlnx}\Rightarrow\frac{\mathrm{y}'}{\mathrm{y}}=\mathrm{lnx}+\mathrm{1}…
Question Number 162116 by naka3546 last updated on 26/Dec/21 $${A}\:{function}\:\:{f}\:\:\:{is}\:\:{such}\:\:{that}\:\:{f}\::\:\mathbb{R}\:\rightarrow\:\mathbb{R}\:\:{where} \\ $$$$\:\:\:{f}\left({xy}+\mathrm{1}\right)\:=\:{f}\left({x}\right)\centerdot{f}\left({y}\right)−{f}\left({y}\right)−{x}+\mathrm{2}\:\:,\:\:\forall{x},{y}\:\in\:\mathbb{R}\:. \\ $$$${Find}\:\:{value}\:\:{of}\:\:\mathrm{10}\centerdot{f}\left(\mathrm{2017}\right)+{f}\left(\mathrm{0}\right)\:. \\ $$ Answered by Rasheed.Sindhi last updated on 27/Dec/21 $${f}\left({xy}+\mathrm{1}\right)\:=\:{f}\left({x}\right)\centerdot{f}\left({y}\right)−{f}\left({y}\right)−{x}+\mathrm{2}\:\:,\:\:\forall{x},{y}\:\in\:\mathbb{R}\:. \\…