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Question Number 112844 Answers: 2 Comments: 1

Find general solution (1)(((sin x)/(1+y))) (dy/dx) = cos x (2) X = tan^(−1) ((2/(11)))+cot^(−1) (((24)/7))+tan^(−1) ((1/3)) find X .

$$\:\mathrm{Find}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\left(\mathrm{1}\right)\left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{1}+\mathrm{y}}\right)\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{cos}\:\mathrm{x} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{X}\:=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{11}}\right)+\mathrm{cot}^{−\mathrm{1}} \left(\frac{\mathrm{24}}{\mathrm{7}}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{3}}\right) \\ $$$$\:\:\mathrm{find}\:\mathrm{X}\:. \\ $$

Question Number 112840 Answers: 1 Comments: 0

solve y′′−y′+e^(2x) y = 0

$$\mathrm{solve}\:\mathrm{y}''−\mathrm{y}'+\mathrm{e}^{\mathrm{2x}} \mathrm{y}\:=\:\mathrm{0} \\ $$

Question Number 112838 Answers: 1 Comments: 0

What is the sum of all the solutions of the equation ∣2x+8∣^2 −∣9x+36∣−9=0

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{solutions} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{equation}\:\mid\mathrm{2x}+\mathrm{8}\mid^{\mathrm{2}} −\mid\mathrm{9x}+\mathrm{36}\mid−\mathrm{9}=\mathrm{0} \\ $$

Question Number 112818 Answers: 0 Comments: 3

Question Number 112810 Answers: 2 Comments: 0

Question Number 112808 Answers: 1 Comments: 0

Question Number 112809 Answers: 1 Comments: 0

Question Number 112805 Answers: 1 Comments: 0

If x=(((√(a+2b))+ (√(a−2b)))/( (√(a+2b))− (√(a−2b)))), then the value of bx^2 −ax+b is

$$\mathrm{If}\:\mathrm{x}=\frac{\sqrt{\mathrm{a}+\mathrm{2b}}+\:\sqrt{\mathrm{a}−\mathrm{2b}}}{\:\sqrt{\mathrm{a}+\mathrm{2b}}−\:\sqrt{\mathrm{a}−\mathrm{2b}}},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{bx}^{\mathrm{2}} −\mathrm{ax}+\mathrm{b}\:\mathrm{is} \\ $$

Question Number 112804 Answers: 1 Comments: 0

If ((97)/(19))= a+(1/(b+(1/c))), where a,b and c are positive integers, then what is the sum of a,b and c?

$$\mathrm{If}\:\frac{\mathrm{97}}{\mathrm{19}}=\:\mathrm{a}+\frac{\mathrm{1}}{\mathrm{b}+\frac{\mathrm{1}}{\mathrm{c}}},\:\mathrm{where}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}\:\mathrm{are} \\ $$$$\mathrm{positive}\:\mathrm{integers},\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{and}\:\mathrm{c}? \\ $$

Question Number 112803 Answers: 1 Comments: 0

If x+y+z=0, then the value of ((x^2 +y^2 +z^2 )/(x^2 −yz)) is

$$\mathrm{If}\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{0},\: \\ $$$$\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} −\mathrm{yz}}\:\mathrm{is} \\ $$

Question Number 112802 Answers: 3 Comments: 0

If xy+yz+zx=0, then ((1/(x^2 −yz))+(1/(y^2 −zx))+(1/(z^2 −xy)))(x,y,z ≠ 0) is equal to

$$\mathrm{If}\:\mathrm{xy}+\mathrm{yz}+\mathrm{zx}=\mathrm{0},\:\mathrm{then} \\ $$$$ \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} −\mathrm{yz}}+\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} −\mathrm{zx}}+\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} −\mathrm{xy}}\right)\left(\mathrm{x},\mathrm{y},\mathrm{z}\:\neq\:\mathrm{0}\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to} \\ $$$$ \\ $$

Question Number 112798 Answers: 1 Comments: 0

Question Number 112796 Answers: 0 Comments: 2

For any real numbers x,y and z if x+y+z=2, then prove that xyz≥8(1−x)(1−y)(1−z).

$${For}\:{any}\:{real}\:{numbers}\:{x},{y}\:{and}\:{z}\:{if} \\ $$$${x}+{y}+{z}=\mathrm{2},\:{then}\:{prove}\:{that} \\ $$$${xyz}\geqslant\mathrm{8}\left(\mathrm{1}−{x}\right)\left(\mathrm{1}−{y}\right)\left(\mathrm{1}−{z}\right). \\ $$

Question Number 112795 Answers: 1 Comments: 1

Question Number 112792 Answers: 0 Comments: 0

Question Number 112782 Answers: 3 Comments: 0

without L′Hopital lim_(x→π) ((cos ((x/2)))/(x−π))

$$\mathrm{without}\:\mathrm{L}'\mathrm{Hopital} \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)}{\mathrm{x}−\pi} \\ $$

Question Number 112797 Answers: 2 Comments: 0

....calculus... evaluate i: ∫_0 ^( (π/2)) x(√( tan(x))) dx= ??? ii:∫_0 ^( ∞) ((ln(x))/(1+x^2 +x^4 ))dx =??? m.n.july 1970

$$\:\:\:\:\:\:\:\:\:....{calculus}... \\ $$$$\:\:\:{evaluate} \\ $$$$ \\ $$$${i}:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}\sqrt{\:{tan}\left({x}\right)}\:{dx}=\:???\: \\ $$$${ii}:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} +{x}^{\mathrm{4}} }{dx}\:=???\: \\ $$$$\:\:\:{m}.{n}.{july}\:\mathrm{1970} \\ $$

Question Number 112780 Answers: 1 Comments: 1

Question Number 112773 Answers: 1 Comments: 0

∫(( (√x))/(x^3 +1))dx Please help

$$\int\frac{\:\sqrt{{x}}}{{x}^{\mathrm{3}} +\mathrm{1}}{dx} \\ $$$${Please}\:{help} \\ $$

Question Number 112754 Answers: 0 Comments: 0

Question Number 112751 Answers: 1 Comments: 0

Question Number 112746 Answers: 3 Comments: 2

If z = −i is the root of the equation z^3 +k.z^2 +(8+2(√2) i)z+8i =0 find the other roots

$$\mathrm{If}\:\mathrm{z}\:=\:−\mathrm{i}\:\mathrm{is}\:\mathrm{the}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{z}^{\mathrm{3}} +\mathrm{k}.\mathrm{z}^{\mathrm{2}} +\left(\mathrm{8}+\mathrm{2}\sqrt{\mathrm{2}}\:\mathrm{i}\right)\mathrm{z}+\mathrm{8i}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{other}\:\mathrm{roots} \\ $$

Question Number 112737 Answers: 2 Comments: 1

Given z=−6+2(√3) i find the two least value of n such that z^n .z^− purelly imaginary.

$$\mathrm{Given}\:\mathrm{z}=−\mathrm{6}+\mathrm{2}\sqrt{\mathrm{3}}\:\mathrm{i} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{two}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{z}^{\mathrm{n}} .\overset{−} {\mathrm{z}}\:\mathrm{purelly}\:\mathrm{imaginary}. \\ $$

Question Number 112740 Answers: 1 Comments: 0

Solve differential equation the method of variation of parameters: (d^2 y/dx^2 ) +4y =4 cosec 2x

$$\:\mathrm{Solve}\:\mathrm{differential}\:\mathrm{equation}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of} \\ $$$$\:\mathrm{variation}\:\mathrm{of}\:\mathrm{parameters}: \\ $$$$\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:+\mathrm{4}\boldsymbol{\mathrm{y}}\:=\mathrm{4}\:\boldsymbol{\mathrm{cosec}}\:\mathrm{2}\boldsymbol{\mathrm{x}}\: \\ $$

Question Number 112720 Answers: 2 Comments: 0

Q. y = (xcosx)^x + (xsinx)^(1/x) then find (dy/dx)

$$\boldsymbol{\mathrm{Q}}.\:\boldsymbol{{y}}\:=\:\left(\boldsymbol{{x}\mathrm{cos}{x}}\right)^{\boldsymbol{{x}}} +\:\left(\boldsymbol{{x}\mathrm{sin}{x}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} \:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$

Question Number 112714 Answers: 2 Comments: 0

Q. y = sin^(−1) (((a + bcosx)/(b + acosx))) , then find (dy/dx)

$$\boldsymbol{\mathrm{Q}}.\:\:\boldsymbol{{y}}\:=\:\boldsymbol{\mathrm{sin}}^{−\mathrm{1}} \left(\frac{\boldsymbol{{a}}\:+\:\boldsymbol{{b}\mathrm{cos}{x}}}{\boldsymbol{{b}}\:+\:\boldsymbol{{a}\mathrm{cos}{x}}}\right)\:,\:\:\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{find}}\:\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}} \\ $$

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