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AllQuestion and Answers: Page 1080

Question Number 110920 Answers: 1 Comments: 1

Question Number 110919 Answers: 1 Comments: 0

lim_(n→∞) (Σ_(r=1) ^n (1/(3^r r!))(Π_(k=1) ^r (2k−1)))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{3}^{{r}} {r}!}\left(\underset{{k}=\mathrm{1}} {\overset{{r}} {\prod}}\left(\mathrm{2}{k}−\mathrm{1}\right)\right)\right) \\ $$

Question Number 110301 Answers: 0 Comments: 1

Question Number 110299 Answers: 3 Comments: 0

Question Number 110294 Answers: 1 Comments: 0

∣2x+1∣−∣x−2∣ < 4 find the solution set

$$\mid\mathrm{2}{x}+\mathrm{1}\mid−\mid{x}−\mathrm{2}\mid\:<\:\mathrm{4}\: \\ $$$${find}\:{the}\:{solution}\:{set} \\ $$

Question Number 110293 Answers: 0 Comments: 0

Simplify: ((tan((3π)/7) − 4sin(π/7))/(tan((6π)/7) + 4sin((2π)/7)))

$$\mathrm{Simplify}:\:\:\:\frac{\mathrm{tan}\frac{\mathrm{3}\pi}{\mathrm{7}}\:\:\:−\:\:\mathrm{4sin}\frac{\pi}{\mathrm{7}}}{\mathrm{tan}\frac{\mathrm{6}\pi}{\mathrm{7}}\:\:+\:\:\mathrm{4sin}\frac{\mathrm{2}\pi}{\mathrm{7}}} \\ $$

Question Number 110288 Answers: 1 Comments: 0

Question Number 110287 Answers: 3 Comments: 2

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

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

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