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Question Number 27204 Answers: 1 Comments: 0
$$\mathrm{if}\:{g}\left({x}\right)={f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right) \\ $$$$\mathrm{and}\:{f}^{\left(\mathrm{2}\right)} \left({x}\right)<\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{increasing}\:\mathrm{in}\:\left(\mathrm{0},\mathrm{1}/\mathrm{2}\right)\:\mathrm{and} \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{in}\:\left(\mathrm{1}/\mathrm{2},\mathrm{1}\right) \\ $$
Question Number 27198 Answers: 1 Comments: 0
Question Number 27197 Answers: 1 Comments: 1
Question Number 27203 Answers: 2 Comments: 0
$$\mathrm{Let}\:{S}\:\subset\:\left(\mathrm{0},\:\pi\right)\:\mathrm{denote}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{x} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{8}^{\mathrm{1}+\mid\mathrm{cos}\:{x}\mid+\mathrm{cos}^{\mathrm{2}} {x}+\mid\mathrm{cos}^{\mathrm{3}} {x}\mid+...\:\mathrm{to}\:\infty} =\:\mathrm{4}^{\mathrm{3}} \\ $$$$\mathrm{then}\:{S}\:=\: \\ $$
Question Number 27202 Answers: 1 Comments: 0
Question Number 27527 Answers: 0 Comments: 1
$$\sqrt{\mathrm{5}}=\mathrm{2}.\mathrm{236}\:{then}\:{the}\:{valve}\:{of}\:\mathrm{100}/\sqrt{\mathrm{125}}=? \\ $$
Question Number 27526 Answers: 1 Comments: 0
$$\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{16}} ×\left(\mathrm{256}\right)^{\mathrm{0}.\mathrm{09}} =? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Question Number 27189 Answers: 1 Comments: 0
$${let}\:{give}\:{S}_{{n}\:} =\:\sum_{{p}=\mathrm{1}} ^{{p}={n}} \:{arctan}\:\left(\frac{\mathrm{1}}{\mathrm{2}{p}^{\mathrm{2}} }\:\right)\:\:{find}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \:\:. \\ $$
Question Number 27187 Answers: 0 Comments: 1
$${find}\:{I}=\:\:\int_{\mathrm{0}} ^{\propto} \:\frac{{cosx}}{{cosh}\left({x}\right)}{dx} \\ $$
Question Number 27186 Answers: 1 Comments: 1
$${find}\:{I}=\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{{cosx}\:+\mathrm{2}{sinx}}\:. \\ $$
Question Number 27185 Answers: 0 Comments: 0
$${find}\:\:\int\int_{{D}} \left({x}+{y}\right)^{\mathrm{2}} \:{e}^{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy}\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}\:} /\mathrm{0}<{x}<\mathrm{1}\:{and}\:\mathrm{0}<{y}<\mathrm{1}−{x}\:\right\}. \\ $$
Question Number 27184 Answers: 0 Comments: 1
$${calculate}\:{in}\:{terms}\:{of}\:{x}\:\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}\:}} \frac{{dt}}{\mathrm{1}+{xsint}}\:. \\ $$
Question Number 27183 Answers: 1 Comments: 0
$${find}\:{the}\:{value}\:{of}\:{I}=\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}−\mathrm{1}}{{lnt}}{dt}\:. \\ $$
Question Number 27182 Answers: 0 Comments: 1
$$\:{find}\:{the}\:{value}\:{of}\:{I}_{{a}} =\:\int\int_{{D}_{{a}} } {e}^{−\frac{{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }{\mathrm{2}}} {dxdy}\:\:{with} \\ $$$${D}_{{a}} \:=\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \:/\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \leqslant\:{a}^{\mathrm{2}} \:\:\right\} \\ $$
Question Number 27168 Answers: 0 Comments: 4
Question Number 27159 Answers: 0 Comments: 0
$$\sqrt{\mathrm{1}−{x}^{\mathrm{6}\:} \:}\:+\sqrt{\mathrm{1}−{y}^{\mathrm{6}} }\:={k}^{\mathrm{3}} \left({x}^{\mathrm{3}} −{y}^{\mathrm{3}} \right)\:\:\:{then}\:{prove}\:{that}\:\:\:\frac{{dy}}{{dx}}=\frac{{x}^{\mathrm{2}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{{y}^{\mathrm{2}} \sqrt{\mathrm{1}−{y}^{\mathrm{2}\Delta} }} \\ $$$$ \\ $$$$ \\ $$
Question Number 27144 Answers: 1 Comments: 1
$${Let}\:{A}=\left\{{x},{y},{z}\right\}\:{and}\:{B}=\left\{\mathrm{1},\mathrm{2}\right\}.\:{Find} \\ $$$${the}\:{number}\:{of}\:{relations}\:{from}\:{A}\:{to} \\ $$$${B}. \\ $$
Question Number 27128 Answers: 1 Comments: 0
$${A}\:{body}\:{resting}\:{on}\:{a}\:{rough} \\ $$$${horizontal}\:{plane}\:{require}\:{a}\:{pull}\:{of} \\ $$$$\mathrm{18}{N}\:{inclined}\:{at}\:\mathrm{30}°\:{to}\:{the}\:{plane} \\ $$$${first}\:{to}\:{move}\:{it}.{It}\:{was}\:{found} \\ $$$${that}\:{a}\:{push}\:{of}\:\mathrm{22}{N}\:{inclined}\:{at}\:\mathrm{30}° \\ $$$${to}\:{the}\:{plane}\:{just}\:{moved}\:{the}\:{body}. \\ $$$${Determine}\:{the}\:{weight}\:{and}\: \\ $$$${coefficient}\:{of}\:{friction}. \\ $$
Question Number 27117 Answers: 1 Comments: 0
Question Number 27112 Answers: 0 Comments: 2
Question Number 27104 Answers: 0 Comments: 1
$$\mathrm{sin45}^{{o}\:} \mathrm{cos45}^{{o}} +\sqrt{\mathrm{3}\:\:\:\mathrm{sin}\:\mathrm{60}°=?} \\ $$
Question Number 27103 Answers: 0 Comments: 1
$$\mathrm{the}\:\mathrm{intrest}\:\mathrm{on}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{money}\:\mathrm{at}\:\mathrm{the} \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{6}.\mathrm{25}\:\mathrm{year}\:\mathrm{was}\:\frac{\mathrm{5}}{\mathrm{16}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{itself}.\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{percent}? \\ $$
Question Number 27102 Answers: 1 Comments: 0
Question Number 27101 Answers: 1 Comments: 0
Question Number 27111 Answers: 1 Comments: 0
Question Number 27098 Answers: 0 Comments: 2
$${let}\:{give}\:{S}\left({x}\right)\:=\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{{x}^{{n}} }{{n}}\:\:{and}\:\:{W}\left({x}\right)=\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\left(−\mathrm{1}\right)^{{n}} {x}^{{n}} }{{n}^{\mathrm{2}} } \\ $$$${calculate}\:\:\:{S}\left({x}\right).{W}\left({x}\right).\:\:\:{in}\:{that}\:{we}\:{know}\:/{x}/<\mathrm{1}. \\ $$
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