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Question Number 192746 Answers: 1 Comments: 0

Let G be the group ({1, ı, −1, −ı}, ∙) and let H ≤ (+_− 1, ∙), show that θ:G→H is an Isomorphism. Hello!

$$\mathrm{Let}\:\mathrm{G}\:\mathrm{be}\:\mathrm{the}\:\mathrm{group}\:\left(\left\{\mathrm{1},\:\imath,\:−\mathrm{1},\:−\imath\right\},\:\centerdot\right) \\ $$$$\mathrm{and}\:\mathrm{let}\:\mathrm{H}\:\leqslant\:\left(\underset{−} {+}\mathrm{1},\:\centerdot\right),\:\mathrm{show}\:\mathrm{that} \\ $$$$\theta:\mathrm{G}\rightarrow\mathrm{H}\:\mathrm{is}\:\mathrm{an}\:\mathrm{Isomorphism}. \\ $$$$ \\ $$$$\mathrm{Hello}! \\ $$

Question Number 192743 Answers: 1 Comments: 0

Calculate: I=∫_0 ^( 4) (∫_(x−4) ^( x−2) e^((x+y)/(x−y)) dy)dx

$${Calculate}: \\ $$$${I}=\int_{\mathrm{0}} ^{\:\mathrm{4}} \left(\int_{{x}−\mathrm{4}} ^{\:{x}−\mathrm{2}} {e}^{\frac{{x}+{y}}{{x}−{y}}} {dy}\right){dx} \\ $$

Question Number 192738 Answers: 2 Comments: 0

Find the supremum and infimum of each of the following sequence a) {((n−1)/(2n))} b) {(((−)^n n)/(2n+1))} c){((1+(−)^n )/3)} d) {sin((nπ)/2)} e) {(1/n) − sin((nπ)/2)} f) {(1+(1/(2n)))cos((nπ)/3)} Help!

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{supremum}\:\mathrm{and}\:\mathrm{infimum} \\ $$$$\mathrm{of}\:\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence} \\ $$$$ \\ $$$$\left.\mathrm{a}\left.\right)\left.\:\left\{\frac{\mathrm{n}−\mathrm{1}}{\mathrm{2n}}\right\}\:\:\:\:\mathrm{b}\right)\:\left\{\frac{\left(−\right)^{\mathrm{n}} \mathrm{n}}{\mathrm{2n}+\mathrm{1}}\right\}\:\:\:\:\mathrm{c}\right)\left\{\frac{\mathrm{1}+\left(−\right)^{\mathrm{n}} }{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{d}\left.\right)\:\left\{\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\}\:\:\:\:\mathrm{e}\right)\:\left\{\frac{\mathrm{1}}{\mathrm{n}}\:−\:\mathrm{sin}\frac{\mathrm{n}\pi}{\mathrm{2}}\right\} \\ $$$$ \\ $$$$\left.\mathrm{f}\right)\:\left\{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2n}}\right)\mathrm{cos}\frac{\mathrm{n}\pi}{\mathrm{3}}\right\} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192737 Answers: 1 Comments: 0

Prove that the sequence {a_n } is null when {a_n } is given by ((n^3 +2n^2 −1)/(n^4 −n^2 +2)) Help!

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{null} \\ $$$$\mathrm{when}\:\left\{\mathrm{a}_{\mathrm{n}} \right\}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\frac{\mathrm{n}^{\mathrm{3}} +\mathrm{2n}^{\mathrm{2}} −\mathrm{1}}{\mathrm{n}^{\mathrm{4}} −\mathrm{n}^{\mathrm{2}} +\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192733 Answers: 1 Comments: 0

Question Number 192732 Answers: 2 Comments: 0

let the closed interval [a,b] be the domain of the function f find the domain of f(x−3) and f(x+3) ?

$${let}\:{the}\:{closed}\:{interval}\:\left[{a},{b}\right]\:{be}\:{the}\:{domain}\:{of}\:{the}\:{function}\:{f}\: \\ $$$${find}\:{the}\:{domain}\:{of}\:{f}\left({x}−\mathrm{3}\right)\:{and}\:{f}\left({x}+\mathrm{3}\right)\:?\:\: \\ $$

Question Number 192721 Answers: 1 Comments: 0

x^3 −3xy^2 =18 3x^2 y−y^3 =26 and what do you recommend to read to deal with such problems

$$ \\ $$$${x}^{\mathrm{3}} −\mathrm{3}{xy}^{\mathrm{2}} =\mathrm{18} \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{26} \\ $$$${and}\:{what}\:{do}\:{you}\:{recommend}\:{to}\:{read}\:{to}\:{deal} \\ $$$${with}\:{such}\:{problems} \\ $$

Question Number 192720 Answers: 4 Comments: 0

Question Number 192715 Answers: 1 Comments: 0

∫(dx/(x^2 (√(x^2 +a^2 ))))=?

$$\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }}=? \\ $$

Question Number 192712 Answers: 1 Comments: 0

∫_(−1/2) ^(1/2) (√(x^2 +1+(√(x^4 +x^2 +1)))) dx =?

$$\:\:\:\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}+\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 192707 Answers: 0 Comments: 0

Is been a while we hear from Mr. W (prof) hope he is fine by Gods grace

$$\:{Is}\:{been}\:{a}\:{while}\:{we}\:{hear}\:{from} \\ $$$$\:{Mr}.\:{W}\:\left({prof}\right)\:{hope}\:{he}\:{is}\:{fine}\:{by}\:{Gods} \\ $$$${grace} \\ $$

Question Number 192705 Answers: 0 Comments: 3

Question Number 192704 Answers: 2 Comments: 0

Question Number 192697 Answers: 1 Comments: 0

Find the value of (9x−(1/(100))x)^3 (9x−(2/(100))x)^3 (9x−(3/(100))x)^3 ...(9x−((2013)/(100))x)^3 .

$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} ...\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$

Question Number 192689 Answers: 2 Comments: 1

a plant grow up 1.67cm in the first week after that it grow up 4% grow up more than the first week every week, how much will grow up in 11th week?

$${a}\:{plant}\:{grow}\:{up}\:\mathrm{1}.\mathrm{67}{cm}\:{in}\:{the}\:{first}\:{week} \\ $$$${after}\:{that}\:{it}\:{grow}\:{up}\:\mathrm{4\%}\:{grow}\:{up}\:{more} \\ $$$${than}\:{the}\:{first}\:{week}\:{every}\:{week},\:{how}\:{much} \\ $$$${will}\:{grow}\:{up}\:{in}\:\mathrm{11}{th}\:{week}? \\ $$

Question Number 192688 Answers: 1 Comments: 0

Prove that : C_n ^k = (1/(2π)) ∫^( π) _( −π) (2cos(θ/2))^n cos[((n/2)−k)θ]dθ

$$\mathrm{Prove}\:\mathrm{that}\:: \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \:=\:\frac{\mathrm{1}}{\mathrm{2}\pi}\:\underset{\:−\pi} {\int}^{\:\:\:\pi} \left(\mathrm{2cos}\frac{\theta}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{cos}\left[\left(\frac{\mathrm{n}}{\mathrm{2}}−\mathrm{k}\right)\theta\right]\mathrm{d}\theta \\ $$

Question Number 192687 Answers: 1 Comments: 0

(1/π)∫_0 ^(2π) xcos(nx)dx Help!

$$\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{xcos}\left(\mathrm{nx}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192676 Answers: 1 Comments: 0

Find: x = ? 1. lg(5x^2 − 6)∙lg(5x − 6) = 0 2. (2x − 5)∙log_3 (1,5 − x) = 0 3. 4^x − 14∙2^x − 32 = 0

$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\:\mathrm{lg}\left(\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{6}\right)\centerdot\mathrm{lg}\left(\mathrm{5x}\:−\:\mathrm{6}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{2}.\:\:\left(\mathrm{2x}\:−\:\mathrm{5}\right)\centerdot\mathrm{log}_{\mathrm{3}} \left(\mathrm{1},\mathrm{5}\:−\:\mathrm{x}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{3}.\:\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{14}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{32}\:=\:\mathrm{0} \\ $$

Question Number 192675 Answers: 1 Comments: 0

Question Number 192668 Answers: 2 Comments: 0

∫_0 ^4 (1/x)e^x dx − ∫_0 ^4 (1/x)e^((1/2)x) dx= ?

$$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{1}}{{x}}{e}^{{x}} {dx}\:−\:\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{1}}{\mathrm{2}}{x}} {dx}=\:? \\ $$

Question Number 192664 Answers: 0 Comments: 0

Question Number 192663 Answers: 1 Comments: 0

Question Number 192661 Answers: 1 Comments: 2

Question Number 192652 Answers: 2 Comments: 0

lim_(x→0) ((1−(√(cos(x))))/(1+cos((√x))))

$${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−\sqrt{{cos}\left({x}\right)}}{\mathrm{1}+{cos}\left(\sqrt{{x}}\right)} \\ $$

Question Number 192651 Answers: 2 Comments: 0

lim_(x→0) ((2−(√(cos(x)))−cos(x))/x^2 )

$$ \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{2}−\sqrt{{cos}\left({x}\right)}−{cos}\left({x}\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 192650 Answers: 2 Comments: 0

lim_(x→0) ((x−sen(x))/(tan^3 (x))) without lhopital rule

$$ \\ $$$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} \frac{{x}−{sen}\left({x}\right)}{{tan}^{\mathrm{3}} \left({x}\right)} \\ $$$${without}\:{lhopital}\:{rule} \\ $$

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