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Question Number 32501 Answers: 1 Comments: 0
$$\left(\mathrm{x}−\mathrm{2y}+\mathrm{3}\right)^{\mathrm{2}} +\left(\mathrm{3x}+\mathrm{4y}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{100} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ellipse}? \\ $$
Question Number 32500 Answers: 1 Comments: 0
$${proof}:\:\left(−{a}\right)\left(−{b}\right)={ab} \\ $$
Question Number 32499 Answers: 2 Comments: 0
$${proof}:\:{a}\left(−{b}\right)=\left(−{a}\right){b}=−\left({ab}\right) \\ $$
Question Number 32496 Answers: 0 Comments: 0
Question Number 32495 Answers: 0 Comments: 0
Question Number 32494 Answers: 0 Comments: 0
Question Number 32493 Answers: 0 Comments: 0
Question Number 32490 Answers: 1 Comments: 0
$${if}\:{f}\left({x}\right)=\mid{x}\mid\:{and}\:{g}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}.{Find} \\ $$$${the}\:{domain}\:{of}\:{gof} \\ $$
Question Number 32489 Answers: 1 Comments: 1
$${find}\:{the}\:{range}\:{of}\:{f}\left({x}\right)=\mathrm{1}+\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$
Question Number 32487 Answers: 0 Comments: 0
$${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$$${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\ $$
Question Number 32486 Answers: 0 Comments: 1
$${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:{sin}\left(\frac{\mathrm{1}}{{k}}\right). \\ $$
Question Number 32485 Answers: 0 Comments: 1
$${let}\:{give}\:\alpha>\mathrm{1}\:{find}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:. \\ $$
Question Number 32484 Answers: 0 Comments: 2
$$ \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+{y}\right)}{\left({x}+{y}\right)}\:{dx}\:{dy} \\ $$
Question Number 32483 Answers: 0 Comments: 2
$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{cosx}}\:. \\ $$
Question Number 32482 Answers: 0 Comments: 0
$${find}\:\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\frac{{sin}^{\mathrm{2}} {t}}{\mathrm{1}−\mathrm{2}{xcost}\:+{x}^{\mathrm{2}} }{dt}\:{with}\:\mid{x}\mid<\mathrm{1}\:. \\ $$
Question Number 32481 Answers: 0 Comments: 0
$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\left(\sqrt{{t}\:}\:−\mathrm{2}\sqrt{{t}+\mathrm{1}}\:+\sqrt{\left.{t}+\mathrm{2}\right)}\:{dt}\right. \\ $$
Question Number 32480 Answers: 0 Comments: 1
$${find}\:\:\int_{\mathrm{0}} ^{\alpha} \:\sqrt{{tanx}}\:{dx}\:{with}\:\mathrm{0}<\alpha<\frac{\pi}{\mathrm{2}}\:. \\ $$
Question Number 32479 Answers: 0 Comments: 0
$${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{3}{x}\:+\mathrm{1}\right)} \\ $$
Question Number 32478 Answers: 0 Comments: 1
$${find}\:\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\frac{\mathrm{1}+{t}^{\mathrm{2}} }{{t}^{\mathrm{2}} }\right){dt} \\ $$
Question Number 32477 Answers: 0 Comments: 1
$${calcilate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$
Question Number 32492 Answers: 0 Comments: 0
Question Number 32474 Answers: 0 Comments: 0
Question Number 32473 Answers: 0 Comments: 0
Question Number 32472 Answers: 0 Comments: 0
Question Number 32471 Answers: 0 Comments: 0
Question Number 32470 Answers: 0 Comments: 0
$$\underset{{x}\rightarrow\infty} {{lim}}\:{x}\left({sec}\left(\frac{\mathrm{1}}{\sqrt{{x}}}\right)\:−\:\mathrm{1}\right)=... \\ $$
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