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Question Number 26222 Answers: 0 Comments: 2

find the value of Σ_(n=1) ^∝ (1/((n+1)(n+2)n^3 )) in terms of ξ(3) we give ξ(x)= Σ_(n=1) ^∝ (1/n^x ) and x>1 (zeta function of Rieman)

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right){n}^{\mathrm{3}} }\:{in}\:{terms}\:{of}\:\xi\left(\mathrm{3}\right) \\ $$$${we}\:{give}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\:{and}\:{x}>\mathrm{1} \\ $$$$\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$

Question Number 26224 Answers: 1 Comments: 1

find the value of x−(1/x).when x^4 +(1/x^4 )=332

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}.\mathrm{when}\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{332} \\ $$

Question Number 26218 Answers: 0 Comments: 2

∫_2 ^4 sinθ dθ

$$\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\mathrm{sin}\theta\:{d}\theta \\ $$

Question Number 26207 Answers: 1 Comments: 0

I think of a two digit number.The sum of the digits is 9. When the number is reversed and subtracted from the original, the result is 45. Find the original number

$$\mathrm{I}\:\mathrm{think}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}.\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{is}\:\mathrm{9}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reversed}\:\mathrm{and}\:\mathrm{subtracted}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{original},\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{45}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{original}\:\mathrm{number} \\ $$

Question Number 26205 Answers: 1 Comments: 1

Question Number 26200 Answers: 1 Comments: 0

Question Number 26198 Answers: 1 Comments: 0

(2x(√x)+x^2 +y^2 )dx+2y(√x)dy=0

$$\left(\mathrm{2}{x}\sqrt{{x}}+{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dx}+\mathrm{2}{y}\sqrt{{x}}{dy}=\mathrm{0} \\ $$

Question Number 26192 Answers: 0 Comments: 3

find the rsdius of convergence for theserie Σ_(n=0) ^∝ (x^n /(2n+1)) and calculate its sum s(x) find the value of Σ_(n=0) ^∝ (1/(2^n (2n+1))) .

$${find}\:{the}\:{rsdius}\:{of}\:{convergence}\:{for}\:{theserie} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\propto} \:\frac{{x}^{{n}} }{\mathrm{2}{n}+\mathrm{1}}\:{and}\:{calculate}\:{its}\:{sum}\:{s}\left({x}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{0}} ^{\propto} \:\:\frac{\mathrm{1}}{\mathrm{2}^{{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)}\:\:. \\ $$

Question Number 26191 Answers: 1 Comments: 0

2(dy/dx)+x=4(√y)

$$\mathrm{2}\frac{{dy}}{{dx}}+{x}=\mathrm{4}\sqrt{{y}} \\ $$

Question Number 26181 Answers: 2 Comments: 0

Find the moment of inertia and the radius of gyration of a circular plate about an axis through its centre,perpendicular to the plane of the plate.

$${Find}\:{the}\:{moment}\:{of}\:{inertia}\:{and} \\ $$$${the}\:{radius}\:{of}\:{gyration}\:{of}\:{a}\: \\ $$$${circular}\:{plate}\:{about}\:{an}\:{axis}\:{through} \\ $$$${its}\:{centre},{perpendicular}\:{to}\:{the} \\ $$$${plane}\:{of}\:{the}\:{plate}. \\ $$

Question Number 26179 Answers: 1 Comments: 0

For an axis passing through the centre of mass of a rectangular plate(along its length).Show that its moment of inertia is ((ML^2 )/(12)) and the radius of gyration is (L/(2(√3).))

$${For}\:{an}\:{axis}\:{passing}\:{through}\:{the} \\ $$$${centre}\:{of}\:{mass}\:{of}\:{a}\:{rectangular} \\ $$$${plate}\left({along}\:{its}\:{length}\right).{Show}\:{that} \\ $$$${its}\:{moment}\:{of}\:{inertia}\:{is}\:\frac{{ML}^{\mathrm{2}} }{\mathrm{12}}\:{and} \\ $$$${the}\:{radius}\:{of}\:{gyration}\:{is}\:\frac{{L}}{\mathrm{2}\sqrt{\mathrm{3}}.} \\ $$

Question Number 26176 Answers: 0 Comments: 1

find the radius of convergence for the serie Σ_(n=0) ^∝ e^(−(√n)) z^n ...z from C.

$${find}\:{the}\:{radius}\:{of}\:{convergence}\:{for}\:{the} \\ $$$${serie}\:\sum_{{n}=\mathrm{0}} ^{\propto} {e}^{−\sqrt{{n}}} \:{z}^{{n}} \:\:...{z}\:{from}\:{C}. \\ $$

Question Number 26174 Answers: 0 Comments: 0

Question Number 26162 Answers: 1 Comments: 0

Find the volume of the solid generated when the region enclosed by y= (√x) y=0 and x=9 about the line x=9

$${Find}\:\:{the}\:{volume}\:\:{of}\:{the}\:{solid}\:{generated}\:{when}\:{the}\:{region}\:\:{enclosed} \\ $$$${by}\:\:{y}=\:\sqrt{{x}} \\ $$$$\:{y}=\mathrm{0}\:\:{and}\:\:{x}=\mathrm{9}\:{about}\:{the}\:\:{line}\:{x}=\mathrm{9} \\ $$

Question Number 26166 Answers: 0 Comments: 0

Question Number 26159 Answers: 1 Comments: 0

If x^2 + y^2 + 2xy + 2x + 2y + k = 0 represents pair of straight lines then find the value of k.

$$\mathrm{If}\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{xy}\:+\:\mathrm{2}{x}\:+\:\mathrm{2}{y}\:+\:{k}\:=\:\mathrm{0} \\ $$$$\mathrm{represents}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{lines}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{k}. \\ $$

Question Number 26156 Answers: 1 Comments: 0

a two digit number is 3 more than 4 times the sum of its digits. if 18 is added to this number .the sum is equal to number obtained by interchanging the digits.find the number

$${a}\:{two}\:{digit}\:{number}\:{is}\:\mathrm{3}\:{more}\:{than} \\ $$$$\mathrm{4}\:{times}\:{the}\:{sum}\:{of}\:{its}\:{digits}.\:{if} \\ $$$$\mathrm{18}\:{is}\:{added}\:{to}\:{this}\:{number}\:.{the}\: \\ $$$${sum}\:{is}\:{equal}\:{to}\:{number}\:{obtained} \\ $$$${by}\:{interchanging}\:{the}\:{digits}.{find}\:{the}\:{number} \\ $$

Question Number 26153 Answers: 1 Comments: 0

ratio of income of two persons is 9 is to 7.ratio of their expenses is 4 is to 3 .every person saves rupees 200. find income of each.

$${ratio}\:{of}\:{income}\:{of}\:{two}\:{persons}\:{is} \\ $$$$\mathrm{9}\:{is}\:{to}\:\mathrm{7}.{ratio}\:{of}\:{their}\:{expenses} \\ $$$${is}\:\mathrm{4}\:{is}\:{to}\:\mathrm{3}\:.{every}\:{person}\:{saves}\: \\ $$$${rupees}\:\mathrm{200}.\:{find}\:{income}\:{of}\:{each}. \\ $$

Question Number 26148 Answers: 2 Comments: 2

Question Number 26147 Answers: 1 Comments: 0

There are 5 more girls than boys in a class. If 2 boys join the class, the ratio of girls to boys will be 5:4. Find the number of of girls in the class.

$$\mathrm{There}\:\mathrm{are}\:\mathrm{5}\:\mathrm{more}\:\mathrm{girls}\:\mathrm{than}\:\mathrm{boys}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}.\:\mathrm{If}\:\mathrm{2}\:\mathrm{boys}\:\mathrm{join} \\ $$$$\mathrm{the}\:\mathrm{class},\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{girls}\:\mathrm{to}\:\mathrm{boys}\:\mathrm{will}\:\mathrm{be}\:\mathrm{5}:\mathrm{4}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{of}\:\mathrm{girls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}. \\ $$

Question Number 26142 Answers: 0 Comments: 0

Prove that If f(x) is Riemann integrable on [a,b] and ∃M>0 s.t. ∀x∈[a,b] (f(x)≠0 and ∣f(x)∣<M and ∣(1/(f(x)))∣<M), then (1/(f(x))) is Riemann integrable on [a,b].

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]\:\mathrm{and} \\ $$$$\:\:\:\:\:\exists{M}>\mathrm{0}\:{s}.{t}.\:\forall{x}\in\left[{a},{b}\right]\:\left({f}\left({x}\right)\neq\mathrm{0}\:{and}\:\mid{f}\left({x}\right)\mid<{M}\:{and}\:\mid\frac{\mathrm{1}}{{f}\left({x}\right)}\mid<{M}\right), \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{{f}\left({x}\right)}\:\mathrm{is}\:\mathrm{Riemann}\:\mathrm{integrable}\:\mathrm{on}\:\left[{a},{b}\right]. \\ $$

Question Number 26143 Answers: 2 Comments: 1

2000^(3000) vs 3000^(2000) who is stronger ?

$$\mathrm{2000}^{\mathrm{3000}} \:\:\boldsymbol{{vs}}\:\mathrm{3000}^{\mathrm{2000}} \\ $$$$ \\ $$$$\:\boldsymbol{{who}}\:\boldsymbol{{is}}\:\boldsymbol{{stronger}}\:? \\ $$

Question Number 26135 Answers: 1 Comments: 1

Prove that b=2asin^2 θ ; when acosθ−bsinθ=c and θ=45°

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{b}=\mathrm{2asin}^{\mathrm{2}} \theta\:; \\ $$$$\mathrm{when}\:\mathrm{acos}\theta−\mathrm{bsin}\theta=\mathrm{c}\:\mathrm{and}\:\theta=\mathrm{45}° \\ $$

Question Number 26133 Answers: 1 Comments: 1

find the value of (C_n ^(0 ) )^2 +(C_n ^1 )^2 +(C_n ^2 )^2 +...(C_n ^n )^2 .

$${find}\:{the}\:{value}\:{of}\:\:\left({C}_{{n}} ^{\mathrm{0}\:\:} \right)^{\mathrm{2}} \:+\left({C}_{{n}} ^{\mathrm{1}} \right)^{\mathrm{2}} \:+\left({C}_{{n}} ^{\mathrm{2}} \right)^{\mathrm{2}} \:+...\left({C}_{{n}} ^{{n}} \right)^{\mathrm{2}} . \\ $$

Question Number 26132 Answers: 0 Comments: 1

let put S_n =Σ_(k=1) ^(k=n) (((−1)^k )/k) find S_(n ) in terms of H_n then lim_(n−>∝) S_n H_n = Σ_(k=1) ^(k=n) (1/k) ( harmonic serie)

$${let}\:{put}\:{S}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{k}={n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}} \\ $$$${find}\:{S}_{{n}\:} {in}\:{terms}\:{of}\:\:{H}_{{n}} \:{then}\:{lim}_{{n}−>\propto} \:{S}_{{n}} \\ $$$${H}_{{n}} \:=\:\sum_{{k}=\mathrm{1}} ^{{k}={n}} \frac{\mathrm{1}}{{k}}\:\:\:\left(\:{harmonic}\:{serie}\right) \\ $$

Question Number 26127 Answers: 1 Comments: 0

y+2y^3 y^((1)) =(x+4yln (y))y^((1))

$${y}+\mathrm{2}{y}^{\mathrm{3}} {y}^{\left(\mathrm{1}\right)} =\left({x}+\mathrm{4}{y}\mathrm{ln}\:\left({y}\right)\right){y}^{\left(\mathrm{1}\right)} \\ $$

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