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Question Number 92518 Answers: 1 Comments: 0

Question Number 92510 Answers: 1 Comments: 1

(1/(D^2 +2)) (sin 2x) ?

$$\frac{\mathrm{1}}{\mathrm{D}^{\mathrm{2}} +\mathrm{2}}\:\left(\mathrm{sin}\:\mathrm{2x}\right)\:?\: \\ $$

Question Number 92511 Answers: 0 Comments: 2

lim_(x→0) (((x)^(1/3) −(x)^(1/5) )/((x)^(1/3) −(x)^(1/4) ))

$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{5}}]{\mathrm{x}}}{\sqrt[{\mathrm{3}}]{\mathrm{x}}−\sqrt[{\mathrm{4}}]{\mathrm{x}}} \\ $$

Question Number 91796 Answers: 1 Comments: 1

Total sum of this below infinite series : 1). (1/(1×2))+(1/(2×3))+(1/(3×4))+...(1/(n(n+1)))=... 2). 0.6+0.06+0.006+...(6/(10^n ))=...

$$\mathrm{Total}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{this}\:\mathrm{below}\:\mathrm{infinite}\:\mathrm{series}\:: \\ $$$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+...\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}=... \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{0}.\mathrm{6}+\mathrm{0}.\mathrm{06}+\mathrm{0}.\mathrm{006}+...\frac{\mathrm{6}}{\mathrm{10}^{\mathrm{n}} }=... \\ $$

Question Number 91786 Answers: 0 Comments: 7

repost question from mr jagoll { ((2+6y = (x/y)−(√(x−2y)))),(((√(x+(√(x−2y)))) = x+3y−2 )) :}

$${repost}\:{question}\:{from} \\ $$$${mr}\:{jagoll} \\ $$$$\begin{cases}{\mathrm{2}+\mathrm{6}{y}\:=\:\frac{{x}}{{y}}−\sqrt{{x}−\mathrm{2}{y}}}\\{\sqrt{{x}+\sqrt{{x}−\mathrm{2}{y}}}\:=\:{x}+\mathrm{3}{y}−\mathrm{2}\:}\end{cases} \\ $$

Question Number 91785 Answers: 0 Comments: 5

given these bellow sequenses . find fifth term 1). (1/5), (1/4) , (3/(11)), (2/7),... 2). (3/5), ((−9)/(11)) , ((−25)/(19)), ((57)/(35)),... 3). (1/6), (7/(11)) , ((13)/(16)), ((19)/(21)),... 4). 4,− (2/3) , −(4/(13)),− (1/5),... 5). 2, 9 , 28 , 65,...

$$\mathrm{given}\:\:\mathrm{these}\:\mathrm{bellow}\:\mathrm{sequenses}\:.\: \\ $$$$\mathrm{find}\:\mathrm{fifth}\:\mathrm{term} \\ $$$$ \\ $$$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{5}},\:\frac{\mathrm{1}}{\mathrm{4}}\:,\:\frac{\mathrm{3}}{\mathrm{11}},\:\frac{\mathrm{2}}{\mathrm{7}},... \\ $$$$\left.\mathrm{2}\right).\:\:\frac{\mathrm{3}}{\mathrm{5}},\:\frac{−\mathrm{9}}{\mathrm{11}}\:,\:\frac{−\mathrm{25}}{\mathrm{19}},\:\frac{\mathrm{57}}{\mathrm{35}},... \\ $$$$\left.\mathrm{3}\right).\:\:\:\frac{\mathrm{1}}{\mathrm{6}},\:\frac{\mathrm{7}}{\mathrm{11}}\:,\:\frac{\mathrm{13}}{\mathrm{16}},\:\frac{\mathrm{19}}{\mathrm{21}},... \\ $$$$\left.\mathrm{4}\right).\:\:\:\mathrm{4},−\:\frac{\mathrm{2}}{\mathrm{3}}\:,\:−\frac{\mathrm{4}}{\mathrm{13}},−\:\frac{\mathrm{1}}{\mathrm{5}},... \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{2},\:\mathrm{9}\:,\:\mathrm{28}\:,\:\mathrm{65},... \\ $$

Question Number 91783 Answers: 0 Comments: 1

1). (1/2), (2/3), (3/4) , (4/5), ..., .... 2). 4,6,10,18,34,...,.... 3). 5,7,11,19,35,...,.... 4). 4,6,10,18,34,...,.... 5). 4,11,30,85,248,...,...

$$\left.\mathrm{1}\right).\:\:\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{3}}{\mathrm{4}}\:,\:\frac{\mathrm{4}}{\mathrm{5}},\:...,\:.... \\ $$$$\left.\mathrm{2}\right).\:\:\mathrm{4},\mathrm{6},\mathrm{10},\mathrm{18},\mathrm{34},...,.... \\ $$$$\left.\mathrm{3}\right).\:\:\mathrm{5},\mathrm{7},\mathrm{11},\mathrm{19},\mathrm{35},...,.... \\ $$$$\left.\mathrm{4}\right).\:\:\mathrm{4},\mathrm{6},\mathrm{10},\mathrm{18},\mathrm{34},...,.... \\ $$$$\left.\mathrm{5}\right).\:\:\mathrm{4},\mathrm{11},\mathrm{30},\mathrm{85},\mathrm{248},...,... \\ $$

Question Number 91774 Answers: 0 Comments: 0

∫_0 ^∞ ((sin^k (x))/x^k )dx for any k>0

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}\:^{{k}} \left({x}\right)}{{x}^{{k}} }{dx}\:{for}\:{any}\:{k}>\mathrm{0} \\ $$

Question Number 91771 Answers: 0 Comments: 1

∫_0 ^∞ ((sin^3 (x))/x^2 )dx

$$\int_{\mathrm{0}} ^{\infty} \frac{{sin}^{\mathrm{3}} \left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 91770 Answers: 1 Comments: 2

y′′+3y=x^3 +3x