Question and Answers Forum
All Questions Topic List
AllQuestion and Answers: Page 1004
Question Number 116767 Answers: 0 Comments: 1
$${if}\:\:{A}×{B}=\mathrm{0}\:{how}\:{to}\:{prove}\:{A}=\mathrm{0}\:{or}\:{B}=\mathrm{0} \\ $$
Question Number 116756 Answers: 2 Comments: 0
$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{x}−\mathrm{2}}}{\mathrm{x}−\mathrm{2}}\:=? \\ $$
Question Number 116753 Answers: 1 Comments: 0
$${if}\:\mathrm{4}^{{x}} =\mathrm{8}{x}\:{find}\:{x} \\ $$
Question Number 116746 Answers: 1 Comments: 0
$$\mathrm{Find}\:\mathrm{an}\:\mathrm{orthogonal}\:\mathrm{matrix}\:\mathrm{A}\:\mathrm{whose} \\ $$$$\mathrm{first}\:\mathrm{row}\:\mathrm{is}\:\mathrm{u}_{\mathrm{1}} =\:\left(\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{2}}{\mathrm{3}}\right). \\ $$
Question Number 116744 Answers: 4 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\frac{\:{nice}}{{calculus}}\:... \\ $$$$\:\:{prove}\:\:{that}\::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{−\mathrm{1}} ^{\:\infty} \frac{{e}^{−\mathrm{4}{x}} }{\:\sqrt{{x}+\mathrm{1}}}\:{dx}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:{e}^{\mathrm{4}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{m}.{n}\:.\mathrm{1970}... \\ $$$$ \\ $$
Question Number 116742 Answers: 0 Comments: 0
$${the}\:{curve}\:{y}={f}\left({x}\right)\:{is}\:{rotated}\:{about}\:{the} \\ $$$${x}−{axis}\:{to}\:{form}\:{solid}.{the}\:{volume}\:{of}\:{this} \\ $$$${solid}\:{is}\:\mathrm{0}.\mathrm{5}\pi\left({a}−\mathrm{2}{sina}\:{cosa}\right)\:{for}\:{the}\:{limit} \\ $$$${of}\:\mathrm{0}\leqslant{x}\leqslant{a}.\:{find}\:{the}\:{value}\:{of}\:{a} \\ $$$$ \\ $$
Question Number 116738 Answers: 1 Comments: 1
$${determine}\:{the}\:{area}\:{of}\:{the}\:{region}\:{bounded} \\ $$$${by}\:{y}=\left(\mathrm{2}{x}+\mathrm{6}\right)^{\mathrm{0}.\mathrm{5}\:} {and}\:{y}={x}−\mathrm{1} \\ $$
Question Number 116737 Answers: 1 Comments: 0
$${find}\:{the}\:{lenght}\:{of}\:{the}\:{function}\:{y}={sinx}\: \\ $$$${for}\:\mathrm{0}<{x}<\pi \\ $$$$ \\ $$
Question Number 116710 Answers: 2 Comments: 0
Question Number 116701 Answers: 2 Comments: 2
$$\int\:\frac{\mathrm{dx}}{\mathrm{x}+\mathrm{x}\sqrt{\mathrm{x}}}\:=? \\ $$
Question Number 116700 Answers: 1 Comments: 0
$$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integral}\: \\ $$$$\mathrm{solutions}\:\mathrm{does}\:\mathrm{3x}+\mathrm{5y}=\mathrm{300}\:\mathrm{have}? \\ $$
Question Number 116695 Answers: 2 Comments: 0
$$\mathrm{Solving}\:\mathrm{by}\:\mathrm{Gaussian}\:\mathrm{elimination} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{of} \\ $$$$\mathrm{linear}\:\mathrm{equation}\:\begin{cases}{\mathrm{x}−\mathrm{3y}−\mathrm{2z}=\mathrm{6}}\\{\mathrm{2x}−\mathrm{4y}−\mathrm{3z}=\mathrm{8}}\\{−\mathrm{3x}+\mathrm{6y}+\mathrm{8z}=−\mathrm{5}}\end{cases} \\ $$
Question Number 116687 Answers: 2 Comments: 0
$${Help}\:{please},\:{to}\:{solve}\:{this}\:... \\ $$$${If}\:{f}\left({x}\right)=\mathrm{1}+{x}^{\mathrm{2}} \:\:{for}\:{x}\in\left[−\mathrm{2},\mathrm{2}\right]\:{and}\: \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\mathrm{5}\:\:\:\:\:\:\:\:{otherwise}. \\ $$$${Then}\:{what}\:{is}\:{the}\:{value}\:{of} \\ $$$$\int_{−\mathrm{2}} ^{+\mathrm{2}} {f}\left(\mathrm{2}{x}^{\mathrm{2}} \right){dx}? \\ $$$$ \\ $$
Question Number 116685 Answers: 1 Comments: 0
$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equality}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+...+\left(\mathrm{2p}+\mathrm{1}\right)=\left(\mathrm{p}+\mathrm{1}\right)^{\mathrm{2}\:} \:\:\:\mathrm{p}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{this}\:\mathrm{equality}\:\mathrm{is}\:\mathrm{true}\:\mathrm{when} \\ $$$$\mathrm{we}\:\mathrm{replace}\:\mathrm{p}\:\mathrm{by}\:\mathrm{p}+\mathrm{1} \\ $$
Question Number 116683 Answers: 2 Comments: 0
$$\mathrm{Given}\:\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}=\mathrm{16}\:\:\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{16}=\mathrm{4}^{\mathrm{2}} \:\:\mathrm{and}\:\mathrm{4}\:\mathrm{is}\:\mathrm{the}\:\mathrm{half}\:\mathrm{of}\:\mathrm{8}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{successor}\:\mathrm{of}\:\mathrm{7}. \\ $$$$ \\ $$$$\mathrm{conjecture}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sum}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+...+\mathrm{25} \\ $$
Question Number 116674 Answers: 2 Comments: 1
Question Number 116672 Answers: 2 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{nice}\:\:{calculus}\:... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:\:{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\frac{\pi}{\mathrm{4}}\:\:−\mathscr{A}{rctan}\left({x}\right)\right)\frac{{dx}}{\mathrm{1}−{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{G}}{\mathrm{2}}\:\:\checkmark\:\:\:\: \\ $$$$\:\:\:\:\:\:\: \\ $$$$\mathrm{G}\:{is}\:\:\:{catalan}\:\:{constant}\:... \\ $$$$\:\:\:\:\:\:\:\mathscr{M}.\mathscr{N}.\mathrm{1970} \\ $$$$ \\ $$$$ \\ $$$$\:\:\: \\ $$
Question Number 116669 Answers: 1 Comments: 1
Question Number 116667 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:{nice}\:\:{calculus}... \\ $$$$ \\ $$$$\:\:\:\:\:\:{very}\:{nice}\:\:{integral}:: \\ $$$$\:\:\:\:\:\:\:{demonstrate}::: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{1}−{x}}{\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} \right){log}\left({x}\right)}\:{dx}\overset{???} {=}{log}\left(\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}\right) \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.{m}.{n}.\mathrm{1970}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$
Question Number 116666 Answers: 1 Comments: 0
Question Number 116763 Answers: 0 Comments: 1
$$ \\ $$$$\:\:\:\:\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{3}} }}=? \\ $$
Question Number 116759 Answers: 2 Comments: 0
Question Number 116658 Answers: 2 Comments: 2
Question Number 116717 Answers: 2 Comments: 0
$$\int{xdx} \\ $$
Question Number 116725 Answers: 4 Comments: 3
$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{log}\:_{\mathrm{10}} \left(−\mathrm{1}\right)\:\mathrm{in}\: \\ $$$$\mathrm{complex}\:\mathrm{number} \\ $$
Question Number 116722 Answers: 1 Comments: 0
$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:{e}^{{x}} −\mathrm{5}={k}\:{has}\:{no} \\ $$$${solution} \\ $$
Pg 999 Pg 1000 Pg 1001 Pg 1002 Pg 1003 Pg 1004 Pg 1005 Pg 1006 Pg 1007 Pg 1008
Terms of Service
Privacy Policy
Contact: info@tinkutara.com