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AllQuestion and Answers: Page 124

Question Number 210180 Answers: 1 Comments: 2

Question Number 210172 Answers: 3 Comments: 0

Question Number 210171 Answers: 0 Comments: 0

Find: lim_(n→+∞) (n/((n!)^2 4^n )) Π_(k=1) ^n ((2k−1)^2 + 4) = ?

$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow+\infty} {\mathrm{lim}}\:\:\frac{\mathrm{n}}{\left(\mathrm{n}!\right)^{\mathrm{2}} \:\mathrm{4}^{\boldsymbol{\mathrm{n}}} }\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\prod}}\:\left(\left(\mathrm{2k}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\mathrm{4}\right)\:=\:? \\ $$

Question Number 210157 Answers: 3 Comments: 0

Question Number 210156 Answers: 1 Comments: 0

Question Number 210155 Answers: 1 Comments: 0

Question Number 210142 Answers: 0 Comments: 1

Question Number 210133 Answers: 1 Comments: 0

calcul ∫_0 ^1 [nt^(n−1) (1−t)−t^n ]dt

$${calcul} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left[{nt}^{{n}−\mathrm{1}} \left(\mathrm{1}−{t}\right)−{t}^{{n}} \right]{dt} \\ $$

Question Number 210127 Answers: 1 Comments: 0

Question Number 210126 Answers: 1 Comments: 0

Question Number 210124 Answers: 0 Comments: 0

Question Number 210120 Answers: 2 Comments: 0

Question Number 210112 Answers: 2 Comments: 0

show that ∫_0 ^∞ (x^n /((x+1)(ax+b)))dx=((((b/a))^n −1)/(b−a))𝛑csc(𝛑n) a>0,b>0,∣n∣<1 guys kill this let me see

Question Number 210098 Answers: 5 Comments: 4

show that ∫_0 ^1 ((lnx)/(x^2 −1))dx=(𝛑^2 /8)

$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{lnx}}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\boldsymbol{\mathrm{dx}}=\frac{\boldsymbol{\pi}^{\mathrm{2}} }{\mathrm{8}} \\ $$

Question Number 210095 Answers: 1 Comments: 1

Question Number 210091 Answers: 1 Comments: 2

find Σ_(n=1) ^∞ tan^(−1) ((1/(2n^2 )))=?

$${find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 210087 Answers: 0 Comments: 0

Question Number 210085 Answers: 1 Comments: 0

(1/((1/(2003))+(1/(2004))+(1/(2005))+(1/(2006))+(1/(2007))+(1/(2008))+(1/(2009)))) = ? Help me

$$ \\ $$$$\:\:\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2003}}+\frac{\mathrm{1}}{\mathrm{2004}}+\frac{\mathrm{1}}{\mathrm{2005}}+\frac{\mathrm{1}}{\mathrm{2006}}+\frac{\mathrm{1}}{\mathrm{2007}}+\frac{\mathrm{1}}{\mathrm{2008}}+\frac{\mathrm{1}}{\mathrm{2009}}}\:=\:? \\ $$$$\:\:\:\mathscr{H}{elp}\:{me} \\ $$$$ \\ $$

Question Number 210082 Answers: 1 Comments: 0

prove that ∫_0 ^1 ((ln(1−t+tx^2 ))/(x^2 −1))dx=(sin^(−1) ((√t)))^2 please anyone..

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{tx}}^{\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1}}\mathrm{dx}=\left(\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\sqrt{\boldsymbol{\mathrm{t}}}\right)\right)^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{anyone}}.. \\ $$

Question Number 210081 Answers: 0 Comments: 0

Reduce [(3,(−2),4,7),(2,1,0,(−3)),(2,8,(−8),2) ] into echelon form

$${Reduce}\:\: \\ $$$$ \\ $$$$\:\:\:\begin{bmatrix}{\mathrm{3}}&{−\mathrm{2}}&{\mathrm{4}}&{\mathrm{7}}\\{\mathrm{2}}&{\mathrm{1}}&{\mathrm{0}}&{−\mathrm{3}}\\{\mathrm{2}}&{\mathrm{8}}&{−\mathrm{8}}&{\mathrm{2}}\end{bmatrix}\:\:\:\:{into}\:{echelon}\:{form} \\ $$$$ \\ $$

Question Number 210080 Answers: 1 Comments: 4

Given that det [(a,b,c),(d,e,f),(g,h,i) ]=n find det [((d+2a),(e+2b),(f+2c)),((2a),(2b),(2c)),((4g),(4h),(4i)) ]

$${Given}\:{that}\:\:{det}\:\begin{bmatrix}{{a}}&{{b}}&{{c}}\\{{d}}&{{e}}&{{f}}\\{{g}}&{{h}}&{{i}}\end{bmatrix}={n} \\ $$$$ \\ $$$${find}\:{det}\begin{bmatrix}{{d}+\mathrm{2}{a}}&{{e}+\mathrm{2}{b}}&{{f}+\mathrm{2}{c}}\\{\mathrm{2}{a}}&{\mathrm{2}{b}}&{\mathrm{2}{c}}\\{\mathrm{4}{g}}&{\mathrm{4}{h}}&{\mathrm{4}{i}}\end{bmatrix} \\ $$$$ \\ $$

Question Number 210079 Answers: 0 Comments: 0

Find directional derivatives(D_v )of f(x,y,z)=3xy^3 −2xz^2 in the direction of the v=2i−3j+6k. then Evaluate directional derivatives at the point (3,1,−2)

$${Find}\:{directional}\:{derivatives}\left({D}_{{v}} \right){of}\:\: \\ $$$${f}\left({x},{y},{z}\right)=\mathrm{3}{xy}^{\mathrm{3}} −\mathrm{2}{xz}^{\mathrm{2}} \:\:{in}\:{the}\:{direction}\:{of}\:{the} \\ $$$${v}=\mathrm{2}{i}−\mathrm{3}{j}+\mathrm{6}{k}. \\ $$$${then}\:{Evaluate}\:{directional}\:{derivatives}\: \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{3},\mathrm{1},−\mathrm{2}\right) \\ $$

Question Number 210078 Answers: 1 Comments: 0

Find the directional derivative of f(x,y)=4x^3 −3x^2 y^2 in the direction given by the angle θ=(π/3) and also Evaluate directional derivatives at the point (1,2)

$${Find}\:{the}\:{directional}\:{derivative}\:{of} \\ $$$${f}\left({x},{y}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \:\:\:{in}\:{the}\:{direction}\:{given} \\ $$$${by}\:{the}\:{angle}\:\theta=\frac{\pi}{\mathrm{3}}\: \\ $$$${and}\:{also}\:{Evaluate}\:{directional}\:{derivatives} \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right) \\ $$

Question Number 210072 Answers: 2 Comments: 0

Question Number 210060 Answers: 1 Comments: 0

∫_0 ^(+∞) (n/(sin^2 n+nx^2 ))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{{n}}{{sin}^{\mathrm{2}} {n}+{nx}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$

Question Number 210122 Answers: 1 Comments: 1

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