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Question Number 99824 Answers: 1 Comments: 0

calculate ∫_0 ^1 xe^(−x^2 ) arctan((2/x))dx

$$\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{xe}^{−\mathrm{x}^{\mathrm{2}} } \mathrm{arctan}\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\mathrm{dx} \\ $$

Question Number 99822 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((ch(sinx))/((x^2 +3)^2 ))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{sinx}\right)}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 99820 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((x^2 dx)/((x^4 −x^2 +1)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 99819 Answers: 0 Comments: 0

sove sinx y^′ −cos(2x)y =xe^(−x)

$$\mathrm{sove}\:\:\mathrm{sinx}\:\mathrm{y}^{'} \:−\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{y}\:=\mathrm{xe}^{−\mathrm{x}} \\ $$

Question Number 99818 Answers: 2 Comments: 0

∫_0 ^1 ln(1+(1/(n^2 x^2 )))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \mathrm{x}^{\mathrm{2}} }\right)\mathrm{dx} \\ $$

Question Number 99807 Answers: 3 Comments: 0

Question Number 99804 Answers: 0 Comments: 3

Determine x,y ∈ Z such that 1+2^x +2^(2x+1) = y^2

$${Determine}\:{x},{y}\:\in\:\mathbb{Z}\:{such}\:{that}\: \\ $$$$\mathrm{1}+\mathrm{2}^{{x}} \:+\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} \:=\:{y}^{\mathrm{2}} \: \\ $$

Question Number 99803 Answers: 2 Comments: 0

Π_(k=1) ^∞ (1+(1/k^2 ))=? helpe me

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)=? \\ $$$$\mathrm{helpe}\:\mathrm{me} \\ $$

Question Number 99796 Answers: 1 Comments: 0

Question Number 99793 Answers: 0 Comments: 4

lim_(n→∞) (1(2(3(4(5(6(....(n.)^(1/2) ..)^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) )^(1/2) =?

$$\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\:\left(\mathrm{1}\left(\mathrm{2}\left(\mathrm{3}\left(\mathrm{4}\left(\mathrm{5}\left(\mathrm{6}\left(....\left(\mathrm{n}.\right)^{\frac{\mathrm{1}}{\mathrm{2}}} ..\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} =?\:\:\:\right. \\ $$

Question Number 99789 Answers: 0 Comments: 2

{ ((2^x .3^y = 6)),((3^x .4^y = 12)) :}

$$\begin{cases}{\mathrm{2}^{{x}} .\mathrm{3}^{{y}} \:=\:\mathrm{6}}\\{\mathrm{3}^{{x}} .\mathrm{4}^{{y}} \:=\:\mathrm{12}}\end{cases} \\ $$

Question Number 99779 Answers: 1 Comments: 2

Question Number 99772 Answers: 0 Comments: 13

Apk file for upcoming version with shape editing is available.

$$\mathrm{Apk}\:\mathrm{file}\:\mathrm{for}\:\mathrm{upcoming}\:\mathrm{version} \\ $$$$\mathrm{with}\:\mathrm{shape}\:\mathrm{editing}\:\mathrm{is}\:\mathrm{available}. \\ $$

Question Number 99761 Answers: 1 Comments: 2

Question Number 99766 Answers: 0 Comments: 3

my Quistion represnt these number on the number line (1)7/4 (2)−5/6

$${my}\:{Quistion} \\ $$$${represnt}\:{these}\:{number}\:\:{on}\:\:{the}\:{number}\:\:{line}\:\left(\mathrm{1}\right)\mathrm{7}/\mathrm{4}\:\left(\mathrm{2}\right)−\mathrm{5}/\mathrm{6} \\ $$

Question Number 99744 Answers: 1 Comments: 0

A wire that is highly insulated has a radius of 2.1 mm and a current of 6 Agoes through it. The material used in insulation has thickness of 2.1 mm with a thermal conductivity of 0.2 W/Km. the material used in constructing the wire has a resistivity of 4.2 × 10^(−7) Ωm. assume the the materials reach steady state. Find the difference in temperature between the outer suface and inner surface.

$$\mathrm{A}\:\mathrm{wire}\:\mathrm{that}\:\mathrm{is}\:\mathrm{highly}\:\mathrm{insulated}\:\mathrm{has}\:\mathrm{a}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current} \\ $$$$\mathrm{of}\:\mathrm{6}\:\mathrm{Agoes}\:\mathrm{through}\:\mathrm{it}.\:\mathrm{The}\:\mathrm{material}\:\mathrm{used}\:\mathrm{in}\:\mathrm{insulation}\:\mathrm{has}\:\mathrm{thickness} \\ $$$$\mathrm{of}\:\mathrm{2}.\mathrm{1}\:\mathrm{mm}\:\mathrm{with}\:\mathrm{a}\:\mathrm{thermal}\:\mathrm{conductivity}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\:\mathrm{W}/\mathrm{Km}.\:\mathrm{the}\:\mathrm{material}\:\mathrm{used} \\ $$$$\mathrm{in}\:\mathrm{constructing}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{has}\:\mathrm{a}\:\mathrm{resistivity}\:\mathrm{of}\:\mathrm{4}.\mathrm{2}\:×\:\mathrm{10}^{−\mathrm{7}} \Omega\mathrm{m}.\:\mathrm{assume}\:\mathrm{the}\: \\ $$$$\mathrm{the}\:\mathrm{materials}\:\mathrm{reach}\:\mathrm{steady}\:\mathrm{state}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{in}\:\mathrm{temperature} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{outer}\:\mathrm{suface}\:\mathrm{and}\:\mathrm{inner}\:\mathrm{surface}. \\ $$

Question Number 99742 Answers: 3 Comments: 0

Given A+B+C=180° prove that tan(A/2)tan(B/2)+tan(B/2)tan(C/2)+tan(C/2)tan(A/2)=1

$$\mathcal{G}\mathrm{iven}\:\:\mathrm{A}+\mathrm{B}+\mathrm{C}=\mathrm{180}°\:\:\mathrm{prove}\:\:\mathrm{that} \\ $$$$\mathrm{tan}\frac{\mathrm{A}}{\mathrm{2}}\mathrm{tan}\frac{\mathrm{B}}{\mathrm{2}}+\mathrm{tan}\frac{\mathrm{B}}{\mathrm{2}}\mathrm{tan}\frac{\mathrm{C}}{\mathrm{2}}+\mathrm{tan}\frac{\mathrm{C}}{\mathrm{2}}\mathrm{tan}\frac{\mathrm{A}}{\mathrm{2}}=\mathrm{1} \\ $$

Question Number 99737 Answers: 0 Comments: 0

((3−9x^2 )/(5−25x^2 )) = ((5−125x^3 )/(1−x^2 ))

$$\frac{\mathrm{3}−\mathrm{9x}^{\mathrm{2}} }{\mathrm{5}−\mathrm{25x}^{\mathrm{2}} }\:=\:\frac{\mathrm{5}−\mathrm{125x}^{\mathrm{3}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} } \\ $$

Question Number 99720 Answers: 2 Comments: 5

lim_(x→0) (1/x^2 ) − (1/(tan^2 x)) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:? \\ $$

Question Number 99713 Answers: 2 Comments: 0

Given f(x)=((nx^(n+1) −(n+1)x^n +1)/(x^(p+1) −x^p −x+1)) , x∈R and (n,p)∈N^∗ ×N^∗ a\Calculate lim_(x→+∞) f(x) b\Show that lim_(x→1) =((n(n+1))/(2p))