Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 125

Question Number 210098    Answers: 5   Comments: 4

show that โˆซ_0 ^1 ((lnx)/(x^2 โˆ’1))dx=(๐›‘^2 /8)

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

Question Number 210095    Answers: 1   Comments: 1

Question Number 210091    Answers: 1   Comments: 2

find ฮฃ_(n=1) ^โˆž tan^(โˆ’1) ((1/(2n^2 )))=?

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

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 โˆซ_0 ^1 ((ln(1โˆ’t+tx^2 ))/(x^2 โˆ’1))dx=(sin^(โˆ’1) ((โˆšt)))^2 please anyone..

$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}โˆ’\boldsymbol{\mathrm{t}}+\boldsymbol{\mathrm{tx}}^{\mathrm{2}} \right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} โˆ’\mathrm{1}}\mathrm{dx}=\left(\boldsymbol{\mathrm{sin}}^{โˆ’\mathrm{1}} \left(\sqrt{\boldsymbol{\mathrm{t}}}\right)\right)^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{anyone}}.. \\ $$

Question Number 210081    Answers: 0   Comments: 0

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

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

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 โˆ’2xz^2 in the direction of the v=2iโˆ’3j+6k. then Evaluate directional derivatives at the point (3,1,โˆ’2)

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

Question Number 210078    Answers: 1   Comments: 0

Find the directional derivative of f(x,y)=4x^3 โˆ’3x^2 y^2 in the direction given by the angle ฮธ=(ฯ€/3) and also Evaluate directional derivatives at the point (1,2)

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

Question Number 210072    Answers: 2   Comments: 0

Question Number 210060    Answers: 1   Comments: 0

โˆซ_0 ^(+โˆž) (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

Question Number 210050    Answers: 3   Comments: 0

Question Number 210044    Answers: 1   Comments: 3

lim_(xโ†’โˆž) (1โˆ’(1/2^2 ))(1โˆ’(1/3^2 ))...(1โˆ’(1/n^2 ))=???

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}โˆ’\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)\left(\mathrm{1}โˆ’\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)...\left(\mathrm{1}โˆ’\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)=??? \\ $$

Question Number 210036    Answers: 4   Comments: 0

Question Number 210034    Answers: 1   Comments: 4

Question Number 210032    Answers: 3   Comments: 0

โˆซ_6 ^0 (2+5x)e^((1/3)x) dx

$$\int_{\mathrm{6}} ^{\mathrm{0}} \left(\mathrm{2}+\mathrm{5}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{e}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$

Question Number 210031    Answers: 0   Comments: 0

โˆซ_0 ^(ฯ€/2) ((1โˆ’xcot(x))/x^2 )dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}โˆ’\boldsymbol{\mathrm{xcot}}\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}} \\ $$

Question Number 210025    Answers: 0   Comments: 1

Question Number 210017    Answers: 0   Comments: 0

MATHโˆ’WHIZZKID using kamke find the genral solution for the differential equation 1. x^2 yโ€ฒโ€ฒ+x^2 yโ€ฒโˆ’2y=0 โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ solve this using forbenius mtd 1.x^2 yโ€ฒโ€ฒ+(x^3 โˆ’3x)yโ€ฒ+(4โˆ’2x)y=0 โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ solve the differential eqn by power series 1. yโ€ฒโ€ฒโˆ’2xyโ€ฒ+2py=0 โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ use persevalโ€ฒs theorem to โˆซ_0 ^โˆž ((cos^2 (๐›‚(๐›‘/2)))/((1โˆ’๐›‚^2 )^2 ))dx. โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ evaluate this integral by contour integration 1. โˆซ_0 ^โˆž ((cos^2 (๐›‚(๐›‘/2)))/((1โˆ’๐›‚^2 )^2 ))dx. โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ โˆฎ_c ((1+e^(i๐›‘z) )/((zโˆ’1)^2 (z+1)^2 ))dz cโˆ’upper half plane kliptoโˆ’quantaโŠŽ

$$ \\ $$$$\boldsymbol{\mathrm{MATH}}โˆ’\boldsymbol{\mathrm{WHIZZKID}} \\ $$$$\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{kamke}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{genral}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}''+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}'โˆ’\mathrm{2}\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{forbenius}}\:\boldsymbol{\mathrm{mtd}} \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}''+\left(\boldsymbol{\mathrm{x}}^{\mathrm{3}} โˆ’\mathrm{3}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}}'+\left(\mathrm{4}โˆ’\mathrm{2}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{eqn}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{power}}\:\boldsymbol{\mathrm{series}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{y}}''โˆ’\mathrm{2}\boldsymbol{\mathrm{xy}}'+\mathrm{2}\boldsymbol{\mathrm{py}}=\mathrm{0} \\ $$$$โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ \\ $$$$\boldsymbol{\mathrm{use}}\:\boldsymbol{\mathrm{perseval}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{theorem}}\:\boldsymbol{\mathrm{to}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\alpha}\frac{\boldsymbol{\pi}}{\mathrm{2}}\right)}{\left(\mathrm{1}โˆ’\boldsymbol{\alpha}^{\mathrm{2}} \right)^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}. \\ $$$$โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ \\ $$$$\boldsymbol{\mathrm{evaluate}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{integral}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{contour}}\:\boldsymbol{\mathrm{integration}} \\ $$$$\mathrm{1}.\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\alpha}\frac{\boldsymbol{\pi}}{\mathrm{2}}\right)}{\left(\mathrm{1}โˆ’\boldsymbol{\alpha}^{\mathrm{2}} \right)^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}. \\ $$$$โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’โˆ’ \\ $$$$\oint_{\boldsymbol{\mathrm{c}}} \frac{\mathrm{1}+\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{i}\pi\mathrm{z}}} }{\left(\boldsymbol{\mathrm{z}}โˆ’\mathrm{1}\right)^{\mathrm{2}} \left(\boldsymbol{\mathrm{z}}+\mathrm{1}\right)^{\mathrm{2}} }\boldsymbol{\mathrm{dz}} \\ $$$$\boldsymbol{\mathrm{c}}โˆ’\mathrm{upper}\:\mathrm{half}\:\mathrm{plane} \\ $$$$\boldsymbol{\mathrm{klipto}}โˆ’\boldsymbol{\mathrm{quanta}}\biguplus \\ $$

Question Number 210014    Answers: 2   Comments: 3

Question Number 210013    Answers: 1   Comments: 0

If f(x)= x^2 +ax+b. if f(1)= 3 and and one of the roots of the eqiation f(x)= 0 doubles the other, find the positive values of a and b.

$$\:{If}\:{f}\left({x}\right)=\:{x}^{\mathrm{2}} +{ax}+{b}.\:{if}\:{f}\left(\mathrm{1}\right)=\:\mathrm{3}\:{and}\: \\ $$$$\:{and}\:{one}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{eqiation} \\ $$$$\:{f}\left({x}\right)=\:\mathrm{0}\:{doubles}\:{the}\:{other},\:{find}\:{the} \\ $$$$\:{positive}\:{values}\:{of}\:{a}\:{and}\:{b}. \\ $$

Question Number 210011    Answers: 0   Comments: 0

Find: โˆซ_0 ^( 1) ((ln (cos (((ฯ€x)/2))))/(x^2 + x)) dx = ?

$$\mathrm{Find}:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:\left(\frac{\pi\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}\:\mathrm{dx}\:\:=\:\:? \\ $$

Question Number 209999    Answers: 3   Comments: 0

lim_(xโ†’0) ((e^x โˆ’1)/( (โˆš(1โˆ’cosx)))) =?

$$\:\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}} โˆ’\mathrm{1}}{\:\sqrt{\mathrm{1}โˆ’\boldsymbol{{cosx}}}}\:=? \\ $$

Question Number 209991    Answers: 2   Comments: 0

((10^(log _3 (6)) . 15^(log _3 ((2/3))) )/(6^(log _3 ((2/3))) . 5^(log _3 ((4/3))) )) =?

$$\:\:\:\:\:\frac{\mathrm{10}^{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{6}\right)} .\:\mathrm{15}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)} }{\mathrm{6}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)} .\:\mathrm{5}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{4}}{\mathrm{3}}\right)} }\:=?\: \\ $$

  Pg 120      Pg 121      Pg 122      Pg 123      Pg 124      Pg 125      Pg 126      Pg 127      Pg 128      Pg 129   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com