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AllQuestion and Answers: Page 1612

Question Number 44783 Answers: 1 Comments: 0

(x^2 )^2 +(y^2 )^2 =97.......1 (x^2 )^3 +(y^2 )^3 =793.......2 solve the simultaneous equation

$$\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{2}} =\mathrm{97}.......\mathrm{1} \\ $$$$\left({x}^{\mathrm{2}} \right)^{\mathrm{3}} +\left({y}^{\mathrm{2}} \right)^{\mathrm{3}} =\mathrm{793}.......\mathrm{2} \\ $$$${solve}\:{the}\:{simultaneous}\:{equation} \\ $$

Question Number 44781 Answers: 2 Comments: 0

prove that:− ∫(1/(t(√(1−t^2 ))))dt = ln(1−(√(1−t^2 )))+C

$$\boldsymbol{{prove}}\:\boldsymbol{{that}}:−\:\int\frac{\mathrm{1}}{\boldsymbol{\mathrm{t}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }}\boldsymbol{\mathrm{dt}}\:=\:\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\sqrt{\mathrm{1}−\boldsymbol{\mathrm{t}}^{\mathrm{2}} }\right)+\boldsymbol{\mathrm{C}} \\ $$

Question Number 44779 Answers: 0 Comments: 2

Question Number 44778 Answers: 0 Comments: 0

Question Number 44777 Answers: 0 Comments: 0

Question Number 44795 Answers: 1 Comments: 4

Question Number 44773 Answers: 0 Comments: 0

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Question Number 44765 Answers: 0 Comments: 0

Question Number 44763 Answers: 1 Comments: 1

Question Number 44761 Answers: 0 Comments: 1

Question Number 44749 Answers: 1 Comments: 1

Question Number 44737 Answers: 0 Comments: 0

A and B are two non−singular matrices such that A^6 =I and AB^2 =BA(B≠I). Then value of K for which B^K =I.

$${A}\:{and}\:{B}\:{are}\:{two}\:{non}−{singular}\:{matrices} \\ $$$${such}\:{that}\:{A}^{\mathrm{6}} ={I}\:{and}\:{AB}^{\mathrm{2}} ={BA}\left({B}\neq{I}\right). \\ $$$${Then}\:{value}\:{of}\:{K}\:{for}\:{which}\:{B}^{{K}} ={I}. \\ $$

Question Number 44730 Answers: 1 Comments: 1

Question Number 44729 Answers: 4 Comments: 0

Question Number 44716 Answers: 1 Comments: 0

prove: 1 + 11 + 111 + .... + ((111 ...111)/(n times)) = ((10^(n + 1) − 9n − 10)/(81))

$$\mathrm{prove}:\:\:\:\:\:\mathrm{1}\:+\:\mathrm{11}\:+\:\mathrm{111}\:+\:....\:+\:\frac{\mathrm{111}\:...\mathrm{111}}{\mathrm{n}\:\mathrm{times}}\:\:=\:\:\frac{\mathrm{10}^{\mathrm{n}\:+\:\mathrm{1}} \:−\:\mathrm{9n}\:−\:\mathrm{10}}{\mathrm{81}} \\ $$

Question Number 44712 Answers: 3 Comments: 0

Question Number 44708 Answers: 1 Comments: 0

Let A,B be two n×n matrices such that A+B=AB then prove : AB=BA ?

$${Let}\:{A},{B}\:{be}\:{two}\:{n}×{n}\:{matrices}\:{such} \\ $$$${that}\:{A}+{B}={AB}\:{then}\:{prove}\:: \\ $$$${AB}={BA}\:? \\ $$

Question Number 44702 Answers: 0 Comments: 0

Question Number 44697 Answers: 0 Comments: 0

prove that:− ∫_0 ^∞ (t^(a−1) /(1+t))dt = (𝛑/(sin(𝛑a)))

$$\boldsymbol{{prove}}\:\boldsymbol{{that}}:− \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{{t}}^{\boldsymbol{{a}}−\mathrm{1}} }{\mathrm{1}+\boldsymbol{{t}}}\boldsymbol{{dt}}\:=\:\frac{\boldsymbol{\pi}}{\boldsymbol{{sin}}\left(\boldsymbol{\pi{a}}\right)} \\ $$

Question Number 44704 Answers: 2 Comments: 0

Find the general solution of : 311x − 112y = 73

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\::\:\:\:\:\:\:\:\:\:\:\:\mathrm{311x}\:−\:\mathrm{112y}\:=\:\mathrm{73} \\ $$

Question Number 44706 Answers: 0 Comments: 4

let f_α (x) = ((cos(αx))/(1+x^2 )) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3) give ∫_0 ^x f_α (t) dt at form of serie 4) developp ∫_0 ^∞ f_α (t)dt at integr serie .

$${let}\:{f}_{\alpha} \left({x}\right)\:=\:\frac{{cos}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{give}\:\int_{\mathrm{0}} ^{{x}} \:{f}_{\alpha} \left({t}\right)\:{dt}\:\:{at}\:{form}\:{of}\:{serie}\: \\ $$$$\left.\mathrm{4}\right)\:{developp}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:{f}_{\alpha} \left({t}\right){dt}\:\:{at}\:\:{integr}\:{serie}\:. \\ $$

Question Number 44696 Answers: 1 Comments: 1

∫(1/(1+x^4 ))dx = ?

$$\int\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{4}} }\boldsymbol{\mathrm{dx}}\:=\:? \\ $$

Question Number 44695 Answers: 0 Comments: 2

∫(e^(√(t−1)) /t)dt = ?

$$\int\frac{\boldsymbol{\mathrm{e}}^{\sqrt{\boldsymbol{\mathrm{t}}−\mathrm{1}}} }{\boldsymbol{\mathrm{t}}}\boldsymbol{\mathrm{dt}}\:=\:? \\ $$

Question Number 44691 Answers: 1 Comments: 1

Question Number 44676 Answers: 1 Comments: 6

Question Number 44652 Answers: 2 Comments: 4

Prove that lim_(x→0) (((1+ax)^(1/b) −1)/x) = (a/b).

$${Prove}\:{that}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{ax}\right)^{\frac{\mathrm{1}}{{b}}} −\mathrm{1}}{{x}}\:=\:\frac{{a}}{{b}}. \\ $$

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