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Question Number 42479 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{seven}}\:\boldsymbol{\mathrm{times}}\: \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}.\boldsymbol{\mathrm{if}}\:\mathrm{27}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{substracted}}\: \\ $$$$\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{interchanged}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}} \\ $$$$ \\ $$
Question Number 42481 Answers: 0 Comments: 0
$${find}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{xtant}\right){dt}\:. \\ $$
Question Number 42482 Answers: 0 Comments: 3
$${let}\:{f}\left({x}\right)={e}^{−\mathrm{2}{x}} \:{arctan}\left({x}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$
Question Number 42475 Answers: 0 Comments: 1
$${A}\:{signpost}\:\mathrm{4}.\mathrm{5}{cm}\:{high}\:{is}\:\mathrm{30}{cm}\:{away}\circledast \\ $$$${from}\:{Mrs}\:{Rahup}.{What}\:{is}\:{the} \\ $$$${height}\:{of}\:{the}\:{image}\:{formed}\:{in}\:{her} \\ $$$${retina}?\left({Take}\:{the}\:{eye}\:{lens}-{retina}\right. \\ $$$$\left.{distance}\:{as}\:\mathrm{1}.\mathrm{5}{cm}\right). \\ $$
Question Number 42474 Answers: 0 Comments: 0
Question Number 42473 Answers: 0 Comments: 0
Question Number 42472 Answers: 0 Comments: 0
Question Number 42471 Answers: 0 Comments: 0
Question Number 42470 Answers: 0 Comments: 0
Question Number 42469 Answers: 0 Comments: 0
Question Number 42468 Answers: 0 Comments: 0
Question Number 42463 Answers: 1 Comments: 1
$${let}\:{y}\:\:=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\mathrm{2}}}} \\ $$$${calculate}\:\:\frac{{dy}}{{dx}} \\ $$
Question Number 42458 Answers: 0 Comments: 0
$${a}\:{boy}\:{is}\:{in}\:{front}\:{of}\:{a}\:{wall}.{The}\:{distance}\:{between} \\ $$$${boy}\:{and}\:{wall}\:{is}\:\mathrm{12}{ft}.{the}\:{boy}\:{is}\:{moving}\:{towards} \\ $$$${the}\:{wall}\:{in}\:{such}\:{a}\:{way}\:{that}\:\boldsymbol{{half}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{wall}}\:\boldsymbol{{and}}\:\boldsymbol{{him}}\:\boldsymbol{{is}}\:\boldsymbol{{crossed}}\:\boldsymbol{{in}}\:\boldsymbol{{one}} \\ $$$$\boldsymbol{{minutes}}.\boldsymbol{{S}}{o}\:{find}\:{the}\:{time}\:{the}\:{boy}\:{reach}\:{to}\:{the}\:{wall} \\ $$
Question Number 42448 Answers: 3 Comments: 0
Question Number 42446 Answers: 2 Comments: 1
Question Number 42445 Answers: 0 Comments: 0
$${find}\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{tan}^{{n}} {t}\:{dt}\:\:\:{with}\:{n}\:{integer}\:{natural}\:. \\ $$
Question Number 42435 Answers: 1 Comments: 1
$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{\sqrt{{x}}\:+\sqrt{\mathrm{1}−{x}}} \\ $$
Question Number 42430 Answers: 1 Comments: 2
$${find}\:\int\:\:\:\:\:\:\:\frac{{dx}}{\mathrm{3}+{tan}^{\mathrm{2}} {x}} \\ $$
Question Number 42422 Answers: 1 Comments: 2
Question Number 42408 Answers: 0 Comments: 2
$$\sqrt{{a}−\sqrt{{a}+{x}\:}}+\:\sqrt{{a}+\sqrt{{a}−{x}}\:}\:=\:\mathrm{2}{x} \\ $$$${Solve}\:{for}\:{x}\:{in}\:{terms}\:{of}\:{a} \\ $$
Question Number 42407 Answers: 1 Comments: 1
$$\int\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{tanx}}\:\mathrm{dx} \\ $$
Question Number 42402 Answers: 0 Comments: 0
$${calculate}\:\int\int_{{x}\leqslant{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \leqslant\mathrm{1}} \:\:\:\frac{{dxdy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$
Question Number 42395 Answers: 0 Comments: 1
$${calculate}\:\int\int_{{D}} \:\:\:\:\:\:\frac{{xy}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \right)}{dxdy}\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:/\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:,\mathrm{0}\leqslant{y}\leqslant\mathrm{1},\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant\mathrm{1}\right\} \\ $$
Question Number 42394 Answers: 1 Comments: 1
$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{{t}+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:{dt} \\ $$
Question Number 42392 Answers: 1 Comments: 1
$${calculate}\:\int\:\:\:\frac{{lnx}}{{x}\:+{x}\left({lnx}\right)^{\mathrm{2}} }{dx} \\ $$
Question Number 42391 Answers: 1 Comments: 1
$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}+{tanx}\right){dx} \\ $$
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