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AllQuestion and Answers: Page 1081

Question Number 110286    Answers: 1   Comments: 0

Question Number 110285    Answers: 1   Comments: 0

Question Number 110281    Answers: 1   Comments: 0

Question Number 110280    Answers: 0   Comments: 0

Question Number 110269    Answers: 1   Comments: 4

Question Number 110268    Answers: 0   Comments: 3

Question Number 110265    Answers: 0   Comments: 0

Question Number 110262    Answers: 0   Comments: 0

Solve for X(x,y,z), Y(x,y,z), Z(x,y,z) { (((∂Z/∂y)−(∂Y/∂z)=1−x^2 )),(((∂Z/∂x)−(∂X/∂z)=−(y^2 /2))),(((∂Y/∂x)−(∂X/∂y)=z(2x−y))) :} where { ((X(x,y,0)=0)),((Y(x,y,0)=0)),((Z(x,y,0)=0)) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right),\:\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right) \\ $$$$\begin{cases}{\frac{\partial\mathrm{Z}}{\partial\mathrm{y}}−\frac{\partial\mathrm{Y}}{\partial\mathrm{z}}=\mathrm{1}−\mathrm{x}^{\mathrm{2}} }\\{\frac{\partial\mathrm{Z}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{z}}=−\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{2}}}\\{\frac{\partial\mathrm{Y}}{\partial\mathrm{x}}−\frac{\partial\mathrm{X}}{\partial\mathrm{y}}=\mathrm{z}\left(\mathrm{2x}−\mathrm{y}\right)}\end{cases}\:\mathrm{where}\:\begin{cases}{\mathrm{X}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Y}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\\{\mathrm{Z}\left(\mathrm{x},\mathrm{y},\mathrm{0}\right)=\mathrm{0}}\end{cases} \\ $$

Question Number 110260    Answers: 1   Comments: 0

lim_(x→∞) x cos ((1/x)) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\:\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}}\right)\:? \\ $$

Question Number 110254    Answers: 1   Comments: 0

Given tan α and tan β are the two roots of 2x^2 −x−2=0, then sin(2α+2β)+cos(2α+2β)+tan(2α+2β)=?

$$\mathrm{Given}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{two}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −{x}−\mathrm{2}=\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{sin}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{cos}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{tan}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)=? \\ $$

Question Number 110247    Answers: 1   Comments: 0

Let f(x) = ∫_0 ^( x) e^(−t) dt then f ′′(x) = ??

$$\mathrm{Let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\:{x}} {e}^{−{t}} {dt}\: \\ $$$$\mathrm{then}\:{f}\:''\left({x}\right)\:=\:?? \\ $$

Question Number 110246    Answers: 1   Comments: 0

solve for z∈C: (a+bi)^z =b+ai

$${solve}\:{for}\:{z}\in\mathbb{C}:\:\left({a}+{bi}\right)^{{z}} ={b}+{ai} \\ $$

Question Number 110245    Answers: 1   Comments: 2

solve ∫(dx/( ((c−(√(b−ax))))^(1/3) ))

$${solve}\:\int\frac{{dx}}{\:\sqrt[{\mathrm{3}}]{{c}−\sqrt{{b}−{ax}}}} \\ $$

Question Number 110233    Answers: 0   Comments: 0

Question Number 110227    Answers: 1   Comments: 1

Question Number 110223    Answers: 0   Comments: 4

let :A,B,C,D be anone empety set prove that A×B=C×D↔A=C∧B=D ? help me sir

$${let}\::{A},{B},{C},{D}\:{be}\:{anone}\:{empety}\:{set}\:{prove}\:{that}\: \\ $$$${A}×{B}={C}×{D}\leftrightarrow{A}={C}\wedge{B}={D}\:? \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 110222    Answers: 3   Comments: 0

find the series Σ_(n=2) ^∞ (−1)^n [(1/(3n+1))+(1/(3n−2))]

$${find}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left[\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{3}{n}−\mathrm{2}}\right] \\ $$

Question Number 110219    Answers: 0   Comments: 3

let A and C be two none empety set prove that A⊆B ∧ C ⊆D iff A×C ⊆B×D? help me sir

$${let}\:{A}\:{and}\:{C}\:{be}\:{two}\:{none}\:{empety}\:{set}\:{prove}\:{that} \\ $$$${A}\subseteq{B}\:\wedge\:{C}\:\subseteq{D}\:{iff}\:{A}×{C}\:\subseteq{B}×{D}? \\ $$$${help}\:{me}\:{sir} \\ $$

Question Number 110218    Answers: 1   Comments: 0

Question Number 110215    Answers: 1   Comments: 1

Question Number 110214    Answers: 1   Comments: 0

show that ∫_(−∞) ^(+∞) (((1+(x/π))sin(πx))/(x^2 +4x+5))dx=(1/e^π )

$${show}\:{that}\: \\ $$$$\int_{−\infty} ^{+\infty} \frac{\left(\mathrm{1}+\frac{{x}}{\pi}\right)\mathrm{sin}\left(\pi{x}\right)}{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{5}}{dx}=\frac{\mathrm{1}}{{e}^{\pi} } \\ $$

Question Number 110204    Answers: 1   Comments: 4

Question Number 110203    Answers: 1   Comments: 0

Question Number 110197    Answers: 2   Comments: 4

(−1)^π =? (−1)^((22)/7) =(−1)^(3+(1/7)) =(−1)^3 .(−1)^(1/7) =−(−1)^(1/7) let (−1)^π =t ⇒−(−1)^(1/7) =t ⇒(−1)^(1/7) =−t ⇒(−1)=(−t)^7 ⇒−1=−t^7 ⇒1=t^7 hence t=1 ∴(−1)^π =1 i request all math professionals to check this and if any error then pls comment.

$$\left(−\mathrm{1}\right)^{\pi} =? \\ $$$$\left(−\mathrm{1}\right)^{\frac{\mathrm{22}}{\mathrm{7}}} \\ $$$$=\left(−\mathrm{1}\right)^{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$=\left(−\mathrm{1}\right)^{\mathrm{3}} .\left(−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$=−\left(−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$${let}\:\left(−\mathrm{1}\right)^{\pi} ={t} \\ $$$$\Rightarrow−\left(−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{7}}} ={t} \\ $$$$\Rightarrow\left(−\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{7}}} =−{t} \\ $$$$\Rightarrow\left(−\mathrm{1}\right)=\left(−{t}\right)^{\mathrm{7}} \\ $$$$\Rightarrow−\mathrm{1}=−{t}^{\mathrm{7}} \\ $$$$\Rightarrow\mathrm{1}={t}^{\mathrm{7}} \\ $$$${hence}\:{t}=\mathrm{1} \\ $$$$\therefore\left(−\mathrm{1}\right)^{\pi} =\mathrm{1} \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{request}}\:\boldsymbol{{all}}\:\boldsymbol{{math}} \\ $$$$\boldsymbol{{professionals}}\:\boldsymbol{{to}}\: \\ $$$$\boldsymbol{{check}}\:\boldsymbol{{this}}\:\boldsymbol{{and}}\:\boldsymbol{{if}} \\ $$$$\boldsymbol{{any}}\:\boldsymbol{{error}}\:\boldsymbol{{then}}\:\boldsymbol{{pls}} \\ $$$$\boldsymbol{{comment}}. \\ $$

Question Number 110183    Answers: 3   Comments: 0

(√★)((be)/(math))(√★) log _2 (x)+log _3 (x)+log _4 (x)=1 x=?

$$\:\:\:\sqrt{\bigstar}\frac{{be}}{{math}}\sqrt{\bigstar} \\ $$$$\:\:\mathrm{log}\:_{\mathrm{2}} \left({x}\right)+\mathrm{log}\:_{\mathrm{3}} \left({x}\right)+\mathrm{log}\:_{\mathrm{4}} \left({x}\right)=\mathrm{1} \\ $$$$\:\:\:{x}=? \\ $$

Question Number 110182    Answers: 1   Comments: 2

Solve x^3 +15x−92=0

$$\mathrm{Solve}\:{x}^{\mathrm{3}} +\mathrm{15}{x}−\mathrm{92}=\mathrm{0} \\ $$

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