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Question Number 49952 Answers: 0 Comments: 2

1) simplify A_n = (1/((2+i(√3))^n )) +(1/((2−i(√3))^n )) 2) smplify B_n =(1/((2+(√3))^n )) +(1/((2−(√3))^n )) n integr natural.

$$\left.\mathrm{1}\right)\:{simplify}\:{A}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{2}+{i}\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−{i}\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$$\left.\mathrm{2}\right)\:{smplify}\:\:{B}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural}. \\ $$

Question Number 49950 Answers: 1 Comments: 1

Question Number 49954 Answers: 1 Comments: 1

find f(α) =∫_0 ^1 ((arctan(αx))/(1+α^2 x^2 ))dx 2) calculate ∫_0 ^1 ((arctan(2x))/(1+4x^2 )) dx and ∫_0 ^1 ((arctan(3x))/(1+9x^2 )) dx .

$${find}\:\:\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\mathrm{1}+\alpha^{\mathrm{2}} {x}^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }\:\:{dx}\:\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{3}{x}\right)}{\mathrm{1}+\mathrm{9}{x}^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 49942 Answers: 0 Comments: 1

calculate ∫∫_D (√(x^4 −y^4 ))dxdy with D =[0,1]×[0,1]

$${calculate}\:\int\int_{{D}} \sqrt{{x}^{\mathrm{4}} −{y}^{\mathrm{4}} }{dxdy} \\ $$$${with}\:{D}\:=\left[\mathrm{0},\mathrm{1}\right]×\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 49941 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−x) ln(1+x)dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{e}^{−{x}} {ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 49939 Answers: 0 Comments: 4

find ∫_0 ^(π/2) sinx ln(1+x) dx

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {sinx}\:{ln}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 49938 Answers: 0 Comments: 1

find f(x)=∫_0 ^(π/4) ln(cost+xsint)dt

$${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left({cost}+{xsint}\right){dt} \\ $$

Question Number 49937 Answers: 1 Comments: 2

let u_n =(((−1)^n )/2^n ) + 3n+1 find Σ_(n=0) ^(49) u_n

$${let}\:{u}_{{n}} =\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{{n}} }\:+\:\mathrm{3}{n}+\mathrm{1} \\ $$$${find}\:\sum_{{n}=\mathrm{0}} ^{\mathrm{49}} \:{u}_{{n}} \\ $$

Question Number 49935 Answers: 2 Comments: 1

Question Number 49930 Answers: 1 Comments: 0

Please help me solve this question How many 4 digits number with all digits different are tbere between 1000 and 9999 such tbat the difference between the first and the last digit is plus or ninus 3.

$${Please}\:{help}\:{me}\:{solve}\:{this}\:{question} \\ $$$${How}\:{many}\:\mathrm{4}\:{digits}\:{number}\:{with}\:{all}\:\:{digits}\: \\ $$$${different}\:{are}\:{tbere}\:{between}\:\mathrm{1000}\:{and}\:\mathrm{9999} \\ $$$${such}\:{tbat}\:{the}\:{difference}\:{between}\:{the}\:{first} \\ $$$${and}\:{the}\:{last}\:{digit}\:{is}\:{plus}\:{or}\:{ninus}\:\mathrm{3}. \\ $$$$ \\ $$

Question Number 49927 Answers: 0 Comments: 2

find lim_(x→a^+ ) (x−a)(a^x −x^a ) with a>0 .

$${find}\:{lim}_{{x}\rightarrow{a}^{+} } \:\:\:\:\left({x}−{a}\right)\left({a}^{{x}} −{x}^{{a}} \right)\:\:\:{with}\:{a}>\mathrm{0}\:. \\ $$

Question Number 49922 Answers: 1 Comments: 0

Question Number 49902 Answers: 1 Comments: 1

If F(t)= ∫_0 ^( t) e^(t−y) .ydy. Prove that F(t)= e^t −(1+t).

$${If}\:{F}\left({t}\right)=\:\int_{\mathrm{0}} ^{\:{t}} {e}^{{t}−{y}} .{ydy}. \\ $$$${Prove}\:{that}\:{F}\left({t}\right)=\:{e}^{{t}} −\left(\mathrm{1}+{t}\right). \\ $$

Question Number 49903 Answers: 1 Comments: 1

Question Number 49898 Answers: 0 Comments: 1

Question Number 49877 Answers: 3 Comments: 1

Question Number 49857 Answers: 1 Comments: 4

Please guide me Sir. I was trying to solve this eq for searching possible values of x. eq is : ∣x − 2∣ < 3∣x + 7∣ the range of x whom i got : −((23)/2) < x < −((19)/4) but the result do not satisfy the eq, instead i put x > −4 , they satisfy the eq. please help me out of this pickle. Not because i didn′t try, yet i always stuck in this type of function.

$$\mathrm{Please}\:\mathrm{guide}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{I}\:\mathrm{was}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\mathrm{this}\:\mathrm{eq}\:\mathrm{for}\:\mathrm{searching}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{x}. \\ $$$$\mathrm{eq}\:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid{x}\:−\:\mathrm{2}\mid\:<\:\mathrm{3}\mid{x}\:+\:\mathrm{7}\mid \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}\:\mathrm{whom}\:\mathrm{i}\:\mathrm{got}\::\:\:\:−\frac{\mathrm{23}}{\mathrm{2}}\:<\:{x}\:<\:−\frac{\mathrm{19}}{\mathrm{4}} \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{result}\:\mathrm{do}\:\mathrm{not}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq},\:\mathrm{instead} \\ $$$$\mathrm{i}\:\mathrm{put}\:{x}\:>\:−\mathrm{4}\:,\:\mathrm{they}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq}.\: \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out}\:\mathrm{of}\:\mathrm{this}\:\mathrm{pickle}. \\ $$$$\mathrm{Not}\:\mathrm{because}\:\mathrm{i}\:\mathrm{didn}'\mathrm{t}\:\mathrm{try},\:\mathrm{yet}\:\mathrm{i}\:\mathrm{always} \\ $$$$\mathrm{stuck}\:\mathrm{in}\:\mathrm{this}\:\mathrm{type}\:\mathrm{of}\:\mathrm{function}. \\ $$

Question Number 49851 Answers: 0 Comments: 0