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AllQuestion and Answers: Page 1222

Question Number 90262 Answers: 2 Comments: 2

(y+(√(x^2 +y^2 ))) dx = x dy

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

Question Number 90259 Answers: 1 Comments: 0

a function f is defined on the positive integers satisfies f(1) = 1002 , & f(1)+f(2)+f(3)+ ... +f(n) = n^2 f(n) . find f(2003)

$${a}\:{function}\:{f}\:{is}\:{defined}\:{on}\: \\ $$$${the}\:{positive}\:{integers}\:{satisfies}\: \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{1002}\:,\:\&\:{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+ \\ $$$$...\:+{f}\left({n}\right)\:=\:{n}^{\mathrm{2}} \:{f}\left({n}\right)\:. \\ $$$${find}\:{f}\left(\mathrm{2003}\right)\: \\ $$

Question Number 90258 Answers: 0 Comments: 1

Question Number 90256 Answers: 0 Comments: 0

∫_0 ^π ((cos(2x))/((e^x +cos(x))^2 ))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{{cos}\left(\mathrm{2}{x}\right)}{\left({e}^{{x}} +{cos}\left({x}\right)\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 90252 Answers: 2 Comments: 1

Question Number 90251 Answers: 1 Comments: 2

(1/(1!))+((1^2 +2^2 )/(2!))+((1^2 +2^2 +3^2 )/(3!))+.......= ???

$$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }{\mathrm{2}!}+\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} }{\mathrm{3}!}+.......=\:??? \\ $$

Question Number 90246 Answers: 0 Comments: 0

Question Number 90240 Answers: 0 Comments: 0

solve (d^2 y/dx^2 )+x(dy/dx)+xy=x^3

$${solve} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}\frac{{dy}}{{dx}}+{xy}={x}^{\mathrm{3}} \\ $$$$ \\ $$

Question Number 90233 Answers: 0 Comments: 5

3,4,12,39,103,x (a) 164 (b) 170 (c) 172 (d) 228

$$\mathrm{3},\mathrm{4},\mathrm{12},\mathrm{39},\mathrm{103},\mathrm{x}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{164} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{170} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{172} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{228} \\ $$

Question Number 90226 Answers: 0 Comments: 2

lim_(x→0) (((x^3 (e^x −1)−x^2 )/(xe^x −x)))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{x}^{\mathrm{3}} \left({e}^{{x}} −\mathrm{1}\right)−{x}^{\mathrm{2}} }{{xe}^{{x}} −{x}}\right)=? \\ $$

Question Number 90225 Answers: 0 Comments: 3

x+y+z = 4 z+t+x = −3 y+z+t = 4 t+x+y = 1 find the value of x^2 +y^2 +z^2 +t^2

$$\mathrm{x}+\mathrm{y}+\mathrm{z}\:=\:\mathrm{4} \\ $$$$\mathrm{z}+\mathrm{t}+\mathrm{x}\:=\:−\mathrm{3} \\ $$$$\mathrm{y}+\mathrm{z}+\mathrm{t}\:=\:\mathrm{4} \\ $$$$\mathrm{t}+\mathrm{x}+\mathrm{y}\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{t}^{\mathrm{2}} \: \\ $$

Question Number 90223 Answers: 0 Comments: 0

The number of ways in which 12 books can be put in 3 shelves, 4 on each, is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{12}\:\mathrm{books} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{in}\:\mathrm{3}\:\mathrm{shelves},\:\mathrm{4}\:\mathrm{on}\:\mathrm{each},\:\mathrm{is} \\ $$

Question Number 90222 Answers: 0 Comments: 1

Question Number 90220 Answers: 0 Comments: 0

The number of ways in which 8 distinct toys can be distributed among 5 children is

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:\mathrm{8}\:\mathrm{distinct} \\ $$$$\mathrm{toys}\:\mathrm{can}\:\mathrm{be}\:\mathrm{distributed}\:\mathrm{among}\:\mathrm{5}\: \\ $$$$\mathrm{children}\:\mathrm{is} \\ $$

Question Number 90221 Answers: 0 Comments: 0

There are 3 copies each of 4 different books. The number of ways in which in which they can be arranged in a shelf is

$$\mathrm{There}\:\mathrm{are}\:\mathrm{3}\:\mathrm{copies}\:\mathrm{each}\:\mathrm{of}\:\mathrm{4}\:\mathrm{different} \\ $$$$\mathrm{books}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\mathrm{in}\:\mathrm{which}\:\mathrm{they}\:\mathrm{can}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{shelf}\:\mathrm{is} \\ $$

Question Number 90217 Answers: 0 Comments: 2

let x_(n ) be a sequence with x_0 =2 and x_1 =7 and x_(n+1) =7x_n −12x_(n−1) . Find the general term of x_n .

$${let}\:{x}_{{n}\:} \:{be}\:{a}\:{sequence}\:{with}\:{x}_{\mathrm{0}} =\mathrm{2}\:{and}\:{x}_{\mathrm{1}} =\mathrm{7} \\ $$$${and}\:{x}_{{n}+\mathrm{1}} =\mathrm{7}{x}_{{n}} −\mathrm{12}{x}_{{n}−\mathrm{1}} . \\ $$$${Find}\:{the}\:{general}\:{term}\:{of}\:{x}_{{n}} . \\ $$

Question Number 90212 Answers: 0 Comments: 4

if x^2 = 5x+1 find E = (((x^3 −140) (x^(11) )^(1/(3 )) )/((x^4 +1))^(1/(3 )) )

$${if}\:{x}^{\mathrm{2}} \:=\:\mathrm{5}{x}+\mathrm{1}\: \\ $$$${find}\:{E}\:=\:\frac{\left({x}^{\mathrm{3}} −\mathrm{140}\right)\:\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{11}} }}{\sqrt[{\mathrm{3}\:\:}]{{x}^{\mathrm{4}} +\mathrm{1}}} \\ $$

Question Number 90210 Answers: 1 Comments: 1

lim_(x→(π/3)) (((1−2cos (x))/(π−3x)))=?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}{\pi−\mathrm{3}{x}}\right)=? \\ $$

Question Number 90208 Answers: 0 Comments: 0

Question Number 90200 Answers: 0 Comments: 7

26≡R_1 [37] 1 ≡R_2 [3] 2≡R_3 [5] Find R_1 , R_2 and R_3

$$\mathrm{26}\equiv\mathrm{R}_{\mathrm{1}} \left[\mathrm{37}\right] \\ $$$$\mathrm{1}\:\:\equiv\mathrm{R}_{\mathrm{2}} \left[\mathrm{3}\right] \\ $$$$\mathrm{2}\equiv\mathrm{R}_{\mathrm{3}} \left[\mathrm{5}\right] \\ $$$$\mathrm{Find}\:\mathrm{R}_{\mathrm{1}} ,\:\mathrm{R}_{\mathrm{2}} \mathrm{and}\:\mathrm{R}_{\mathrm{3}} \\ $$

Question Number 90198 Answers: 3 Comments: 3

∫sin(dx)

$$\int{sin}\left({dx}\right)\: \\ $$

Question Number 90195 Answers: 0 Comments: 0

Question Number 90194 Answers: 1 Comments: 0

(x^2 /(x+a))+(√x)=a (a∈R) solve for: x .

$$\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{a}}}+\sqrt{\boldsymbol{\mathrm{x}}}=\boldsymbol{\mathrm{a}}\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}\right) \\ $$$$\mathrm{solve}\:\mathrm{for}:\:\:\mathrm{x}\:\:. \\ $$

Question Number 90196 Answers: 0 Comments: 0

A bag contains 5 balls, 2 green and 3red They are selected without replacement till the remaining balls in the bag are of same colours. Let the random variable X be the number of selections possible 1) Determine the set of values of X 2)Determine the it′s expectation, its variance and its standard deviation.

$$\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{2}\:\mathrm{green}\:\mathrm{and}\:\mathrm{3red} \\ $$$$\mathrm{They}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{till} \\ $$$$\mathrm{the}\:\mathrm{remaining}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\mathrm{of}\:\mathrm{same}\:\mathrm{colours}. \\ $$$$\mathrm{Let}\:\mathrm{the}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{selections}\:\mathrm{possible} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{X} \\ $$$$\left.\mathrm{2}\right)\mathrm{Determine}\:\mathrm{the}\:\mathrm{it}'\mathrm{s}\:\mathrm{expectation},\:\mathrm{its}\:\mathrm{variance} \\ $$$$\mathrm{and}\:\mathrm{its}\:\mathrm{standard}\:\mathrm{deviation}. \\ $$

Question Number 90192 Answers: 1 Comments: 1

∫_0 ^(infinity) (((1−e^(−x) )cosx dx)/x)

$$\int_{\mathrm{0}} ^{\mathrm{infinity}} \frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)\mathrm{cosx}\:\mathrm{dx}}{\mathrm{x}} \\ $$

Question Number 90178 Answers: 1 Comments: 1

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