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Question Number 97226 Answers: 0 Comments: 0

let a_n the sequence wich verify a_n +a_(n+1) =(((−1)^n )/n^2 ) calculate Σ_(n=1) ^∞ a_n x^n

$$\mathrm{let}\:\:\mathrm{a}_{\mathrm{n}} \:\mathrm{the}\:\mathrm{sequence}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{a}_{\mathrm{n}} \:+\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \\ $$

Question Number 97218 Answers: 2 Comments: 0

∫_(−2) ^3 ∣x−2∣ ⌊ (x/2) ⌋ sgn (x−1) dx

$$\underset{−\mathrm{2}} {\overset{\mathrm{3}} {\int}}\:\mid{x}−\mathrm{2}\mid\:\lfloor\:\frac{{x}}{\mathrm{2}}\:\rfloor\:\mathrm{sgn}\:\left({x}−\mathrm{1}\right)\:{dx}\: \\ $$

Question Number 97206 Answers: 2 Comments: 0

Question Number 97200 Answers: 0 Comments: 8

App was updated about a week back to use new backend server for forum as we were facing problems on old server. Please update app to the latest version 2.079 or above. Thanks for ur cooperation. Note: Do not uninstall/reinstall as android removes app data on uninstalls. Backup all inapp saved equation to sdcard before uninstall.

$$\mathrm{App}\:\mathrm{was}\:\mathrm{updated}\:\mathrm{about}\:\:\mathrm{a}\:\mathrm{week} \\ $$$$\mathrm{back}\:\mathrm{to}\:\mathrm{use}\:\mathrm{new}\:\mathrm{backend}\:\mathrm{server} \\ $$$$\mathrm{for}\:\mathrm{forum}\:\mathrm{as}\:\mathrm{we}\:\mathrm{were}\:\mathrm{facing}\:\mathrm{problems}\:\mathrm{on}\:\mathrm{old} \\ $$$$\mathrm{server}. \\ $$$$\mathrm{Please}\:\mathrm{update}\:\mathrm{app}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{latest}\:\mathrm{version}\:\mathrm{2}.\mathrm{079}\:\mathrm{or}\:\mathrm{above}. \\ $$$$\mathrm{Thanks}\:\mathrm{for}\:\mathrm{ur}\:\mathrm{cooperation}. \\ $$$$\mathrm{Note}:\:\mathrm{Do}\:\mathrm{not}\:\mathrm{uninstall}/\mathrm{reinstall} \\ $$$$\mathrm{as}\:\mathrm{android}\:\mathrm{removes}\:\mathrm{app}\:\mathrm{data}\:\mathrm{on} \\ $$$$\mathrm{uninstalls}.\:\mathrm{Backup}\:\mathrm{all}\:\mathrm{inapp} \\ $$$$\mathrm{saved}\:\mathrm{equation}\:\mathrm{to}\:\mathrm{sdcard}\:\mathrm{before} \\ $$$$\mathrm{uninstall}. \\ $$

Question Number 97199 Answers: 1 Comments: 0

lim_(x→0) ((sin x−tan x)/((((1+x^2 ))^(1/(3 )) −1)((√(1+sin x))−1))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{tan}\:\mathrm{x}}{\left(\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{1}\right)\left(\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}−\mathrm{1}\right)}\:=\:? \\ $$

Question Number 97192 Answers: 1 Comments: 4

Question Number 97189 Answers: 0 Comments: 0

Question Number 97182 Answers: 0 Comments: 0

Question Number 97181 Answers: 0 Comments: 0

Question Number 97174 Answers: 0 Comments: 0

Exercise_(−) ABC is a triangle. AB=AC=2 and BC=2(√2). I is midle of [BC]. J is a point such as AJ^(→) =(2/3)AI^(→) . J is the center of gravity of the triangle. 1)a) we define the set(T) of ∀ point M of plane: AM^2 +BM^2 +CM^2 =8. Show that BM^2 +CM^2 =2IM^2 +4 and AM^2 +2IM^2 =3JM^2 +(4/3) b)deduct that AM^2 +BM^2 +CM^2 =3JM^2 +((16)/3) c)Deduct the nature of (T)

$$\underset{−} {{Exercise}} \\ $$$${ABC}\:{is}\:{a}\:{triangle}.\:{AB}={AC}=\mathrm{2}\:{and} \\ $$$${BC}=\mathrm{2}\sqrt{\mathrm{2}}.\:{I}\:{is}\:{midle}\:{of}\:\left[{BC}\right]. \\ $$$${J}\:{is}\:{a}\:{point}\:{such}\:{as}\:\overset{\rightarrow} {{AJ}}=\frac{\mathrm{2}}{\mathrm{3}}\overset{\rightarrow} {{AI}}.\:{J}\:{is} \\ $$$${the}\:{center}\:{of}\:{gravity}\:{of}\:{the}\:{triangle}. \\ $$$$\left.\mathrm{1}\left.\right){a}\right)\:{we}\:{define}\:{the}\:{set}\left({T}\right)\:{of}\:\forall\:{point}\:{M} \\ $$$${of}\:{plane}: \\ $$$${AM}^{\mathrm{2}} +{BM}^{\mathrm{2}} +{CM}^{\mathrm{2}} =\mathrm{8}. \\ $$$${Show}\:{that}\:{BM}^{\mathrm{2}} +{CM}^{\mathrm{2}} =\mathrm{2}{IM}^{\mathrm{2}} +\mathrm{4} \\ $$$${and}\:{AM}^{\mathrm{2}} +\mathrm{2}{IM}^{\mathrm{2}} =\mathrm{3}{JM}^{\mathrm{2}} +\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\left.{b}\right){deduct}\:{that}\: \\ $$$${AM}^{\mathrm{2}} +{BM}^{\mathrm{2}} +{CM}^{\mathrm{2}} =\mathrm{3}{JM}^{\mathrm{2}} +\frac{\mathrm{16}}{\mathrm{3}} \\ $$$$\left.{c}\right){Deduct}\:{the}\:{nature}\:{of}\:\left({T}\right) \\ $$

Question Number 97173 Answers: 1 Comments: 0

Question Number 97157 Answers: 3 Comments: 1

Question Number 97153 Answers: 2 Comments: 0

Question Number 97143 Answers: 1 Comments: 0

Given f(x)=((ax^2 +bx+c)/x) and C_f its graph; Determine the real numbers a, b, and c such that C_f passes through the points A(1;2); B(−4;8) and has a tangent parallel to the x−axis at x=2.

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{x}}\:\mathrm{and}\:\mathcal{C}_{\mathrm{f}} \:\mathrm{its}\:\mathrm{graph}; \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{a},\:\mathrm{b},\:\mathrm{and}\:\mathrm{c}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathcal{C}_{\mathrm{f}} \:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\mathrm{A}\left(\mathrm{1};\mathrm{2}\right);\:\mathrm{B}\left(−\mathrm{4};\mathrm{8}\right)\:\mathrm{and}\:\mathrm{has} \\ $$$$\mathrm{a}\:\mathrm{tangent}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}\:\mathrm{at}\:\mathrm{x}=\mathrm{2}. \\ $$

Question Number 97142 Answers: 2 Comments: 3

prove that cos(mx)cos(ny)=((cos(mx+ny)+cos(mx−ny))/2) ? help me sir ?

$${prove}\:{that}\:{cos}\left({mx}\right){cos}\left({ny}\right)=\frac{{cos}\left({mx}+{ny}\right)+{cos}\left({mx}−{ny}\right)}{\mathrm{2}}\:\:? \\ $$$${help}\:{me}\:{sir}\:? \\ $$

Question Number 97139 Answers: 0 Comments: 1

prove that sinh3x=3sinhx+4sinh^3 x ? help me sir ?

$${prove}\:{that}\:{sinh}\mathrm{3}{x}=\mathrm{3}{sinhx}+\mathrm{4}{sinh}^{\mathrm{3}} {x}\:? \\ $$$${help}\:{me}\:{sir}\:? \\ $$

Question Number 97138 Answers: 0 Comments: 0

if it is H(x,y) ,G(x,y) k class Homogeneous function using aspecific provision find the general solution to the following differential equation y H(x,y)dx+G(x,y)(ydx−xdy)=0 please sir helpe me ? no one help me ?

$${if}\:{it}\:{is}\:{H}\left({x},{y}\right)\:,{G}\left({x},{y}\right)\:{k}\:{class}\:{Homogeneous}\:{function}\:{using}\:{aspecific}\:{provision}\:{find} \\ $$$${the}\:{general}\:{solution}\:{to}\:{the}\:{following}\:{differential}\:{equation} \\ $$$${y}\:{H}\left({x},{y}\right){dx}+{G}\left({x},{y}\right)\left({ydx}−{xdy}\right)=\mathrm{0} \\ $$$$ \\ $$$${please}\:{sir}\:{helpe}\:{me}\:?\: \\ $$$${no}\:{one}\:{help}\:{me}\:? \\ $$

Question Number 97137 Answers: 1 Comments: 2

using aparticular theory ,find the general solution to the following differential equation f(x+y)dx+g(x+y)dy=0 ? help me sir please

$${using}\:{aparticular}\:{theory}\:,{find}\:{the}\:{general}\:{solution}\:{to}\: \\ $$$${the}\:{following}\:{differential}\:{equation}\: \\ $$$${f}\left({x}+{y}\right){dx}+{g}\left({x}+{y}\right){dy}=\mathrm{0}\:? \\ $$$${help}\:{me}\:{sir}\:{please} \\ $$

Question Number 97136 Answers: 0 Comments: 3

Evaluate (3/(1! + 2! + 3!)) + (4/(2! + 3! + 4!)) + ... + ((2001)/(1999! + 2000! + 2001!))

$$\mathrm{Evaluate} \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{1}!\:+\:\mathrm{2}!\:+\:\mathrm{3}!}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{2}!\:+\:\mathrm{3}!\:+\:\mathrm{4}!}\:\:+\:\:...\:+\:\:\frac{\mathrm{2001}}{\mathrm{1999}!\:\:+\:\:\mathrm{2000}!\:\:+\:\:\mathrm{2001}!} \\ $$

Question Number 97135 Answers: 0 Comments: 1

prove that: sin(16x) cot(x)=1+2cos(2x)+2cos(4x)+2cos(6x)+...+2cos(16x)

$${prove}\:{that}: \\ $$$${sin}\left(\mathrm{16}{x}\right)\:{cot}\left({x}\right)=\mathrm{1}+\mathrm{2}{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}{cos}\left(\mathrm{6}{x}\right)+...+\mathrm{2}{cos}\left(\mathrm{16}{x}\right) \\ $$

Question Number 97134 Answers: 0 Comments: 0

find the laplace transform of t^(3/2) erf(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of}\:{t}^{\frac{\mathrm{3}}{\mathrm{2}}} {erf}\left({t}\right) \\ $$

Question Number 97132 Answers: 1 Comments: 1

is the formulla of sin^3 ((π/2)+x)=cos^3 x correct?

$$\mathrm{is}\:\mathrm{the}\:\mathrm{formulla}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\:\:\:\mathrm{correct}? \\ $$

Question Number 97130 Answers: 1 Comments: 0

Question Number 97129 Answers: 0 Comments: 0

Given z=x+iy z∈C z≠0 1\ A, B, and C are the images of z, iz, and (2−i)+z a\ Calculate the lengths AB, AC, and BC. b\ Deduce that the triangle ABC is isosceles and not equilateral. 2\Find z, such that ∣z∣=∣((2+i)/z)∣=∣z−1∣ 3\Given Z, Z∈C such that ((Z−1)/(Z+1))=(((z−1)/(z+1)))^2 a\Express Z in terms of z b\What can we say of the images of Z, z, and (1/z) ?

$$\mathrm{Given}\:\:\mathrm{z}=\mathrm{x}+\mathrm{iy}\:\:\mathrm{z}\in\mathbb{C}\:\:\mathrm{z}\neq\mathrm{0} \\ $$$$\mathrm{1}\backslash\:\mathrm{A},\:\mathrm{B},\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{the}\:\mathrm{images}\:\mathrm{of}\:\mathrm{z},\:\mathrm{iz},\:\mathrm{and}\:\left(\mathrm{2}−\mathrm{i}\right)+\mathrm{z} \\ $$$$\mathrm{a}\backslash\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{lengths}\:\mathrm{AB},\:\mathrm{AC},\:\mathrm{and}\:\mathrm{BC}. \\ $$$$\mathrm{b}\backslash\:\mathrm{Deduce}\:\mathrm{that}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{is}\:\mathrm{isosceles}\:\mathrm{and}\:\mathrm{not} \\ $$$$\mathrm{equilateral}. \\ $$$$\mathrm{2}\backslash\mathrm{Find}\:\mathrm{z},\:\mathrm{such}\:\mathrm{that}\:\mid\mathrm{z}\mid=\mid\frac{\mathrm{2}+\mathrm{i}}{\mathrm{z}}\mid=\mid\mathrm{z}−\mathrm{1}\mid \\ $$$$\mathrm{3}\backslash\mathrm{Given}\:\mathrm{Z},\:\mathrm{Z}\in\mathbb{C}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{Z}−\mathrm{1}}{\mathrm{Z}+\mathrm{1}}=\left(\frac{\mathrm{z}−\mathrm{1}}{\mathrm{z}+\mathrm{1}}\right)^{\mathrm{2}} \\ $$$$\mathrm{a}\backslash\mathrm{Express}\:\mathrm{Z}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{z} \\ $$$$\mathrm{b}\backslash\mathrm{What}\:\mathrm{can}\:\mathrm{we}\:\mathrm{say}\:\mathrm{of}\:\mathrm{the}\:\mathrm{images}\:\mathrm{of}\:\mathrm{Z},\:\mathrm{z},\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{z}}\:? \\ $$

Question Number 97125 Answers: 0 Comments: 0

∫{xtanx+ln∣cos x∣} dx

$$\int\left\{\mathrm{xtanx}+\mathrm{ln}\mid\mathrm{cos}\:\mathrm{x}\mid\right\}\:\mathrm{dx} \\ $$

Question Number 97117 Answers: 1 Comments: 0

lim_(h→0) [ (1/h) ∫_2 ^(2+2h) (√(t^2 +2)) dt ]

$$\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{h}}\:\underset{\mathrm{2}} {\overset{\mathrm{2}+\mathrm{2h}} {\int}}\sqrt{\mathrm{t}^{\mathrm{2}} +\mathrm{2}}\:\mathrm{dt}\:\right]\: \\ $$

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