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Question Number 220353 Answers: 1 Comments: 3

Question Number 220307 Answers: 1 Comments: 0

Question Number 220286 Answers: 3 Comments: 5

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Question Number 220269 Answers: 1 Comments: 0

lim_(t→0) ((C_1 J_ν (t)+C_2 Y_ν (t)+H_ν (t))/(C_1 J_ν (t)+C_2 Y_ν (t)))=?? ν∈R J_ν (z) Bessel function First kind Y_ν (z) Bessel function Second Kind H_ν (z) Struve H function

$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{C}_{\mathrm{1}} {J}_{\nu} \left({t}\right)+{C}_{\mathrm{2}} {Y}_{\nu} \left({t}\right)+\boldsymbol{\mathrm{H}}_{\nu} \left({t}\right)}{{C}_{\mathrm{1}} {J}_{\nu} \left({t}\right)+{C}_{\mathrm{2}} {Y}_{\nu} \left({t}\right)}=?? \\ $$$$\nu\in\mathbb{R} \\ $$$${J}_{\nu} \left({z}\right)\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{First}\:\mathrm{kind} \\ $$$${Y}_{\nu} \left({z}\right)\:\mathrm{Bessel}\:\mathrm{function}\:\mathrm{Second}\:\mathrm{Kind} \\ $$$$\boldsymbol{\mathrm{H}}_{\nu} \left({z}\right)\:\mathrm{Struve}\:\mathrm{H}\:\mathrm{function} \\ $$

Question Number 220266 Answers: 1 Comments: 0

2^a + 2^b + 2^c = 148

$$\mathrm{2}^{\mathrm{a}} \:\:+\:\:\mathrm{2}^{\mathrm{b}} \:\:+\:\:\mathrm{2}^{\mathrm{c}} \:\:=\:\:\mathrm{148} \\ $$

Question Number 220264 Answers: 1 Comments: 0

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Question Number 220257 Answers: 2 Comments: 0

proof that volume of frustum of circular cone is (1/3)h[A1+A2+(√(A1A2)) A_1 and A_2 are areas of base

$${proof}\:{that}\:{volume}\:{of}\:{frustum}\:{of} \\ $$$$\:{circular}\:{cone}\:{is}\:\frac{\mathrm{1}}{\mathrm{3}}{h}\left[{A}\mathrm{1}+{A}\mathrm{2}+\sqrt{{A}\mathrm{1}{A}\mathrm{2}}\right. \\ $$$${A}_{\mathrm{1}} {and}\:{A}_{\mathrm{2}} \:{are}\:\:{areas}\:{of}\:{base} \\ $$

Question Number 220253 Answers: 0 Comments: 0

Question Number 220250 Answers: 3 Comments: 0

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Question Number 220248 Answers: 20 Comments: 0

Question Number 220247 Answers: 2 Comments: 0

Question Number 220246 Answers: 6 Comments: 0

Question Number 220245 Answers: 1 Comments: 0

Question Number 220244 Answers: 3 Comments: 0

Question Number 220243 Answers: 5 Comments: 0

Question Number 220242 Answers: 0 Comments: 0

∫ ((ln x)/((1 + x^2 )^2 )) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\:\:\frac{{ln}\:{x}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)\:^{\mathrm{2}} }\:\:{dx} \\ $$$$ \\ $$

Question Number 220232 Answers: 1 Comments: 0

prove that (π/(16)) < ∫_0 ^( 1 ) (√((x(1−x))/(sin(πx)+cos(πx)+2))) dx<(π/8)

$$ \\ $$$$\:\:\:\:{prove}\:{that} \\ $$$$ \\ $$$$\:\:\frac{\pi}{\mathrm{16}}\:<\:\int_{\mathrm{0}} ^{\:\mathrm{1}\:} \sqrt{\frac{{x}\left(\mathrm{1}−{x}\right)}{{sin}\left(\pi{x}\right)+{cos}\left(\pi{x}\right)+\mathrm{2}}}\:{dx}<\frac{\pi}{\mathrm{8}} \\ $$$$\:\:\:\:\: \\ $$

Question Number 220231 Answers: 4 Comments: 0

Question Number 220224 Answers: 5 Comments: 0

calcul together of definition of and calcul the derive f^ ^′ f(x)= x(√((x−1)/(x+1)))

$${calcul}\:{together}\:{of}\:{definition}\:{of}\:{and} \\ $$$${calcul}\:{the}\:{derive}\:{f}^{\:} \:^{'} \\ $$$${f}\left({x}\right)=\:\:{x}\sqrt{\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}} \\ $$

Question Number 220221 Answers: 0 Comments: 2

Q.The density of an object of mass M is δ and the density of the air is ρ. the mass of of the object is measured with the help of a metal weight of mass m . the density of the metal weight is d. if ρ≪δ them show that the real mass M will be m(1−(ρ/d) )(1+(ρ/δ)) I have managed to M=((m(1−(ρ/d)))/((1−(ρ/δ)))) but I can not figure it to the end please help

$${Q}.{The}\:{density}\:{of}\:{an}\:{object}\:{of}\:{mass}\:{M}\:{is}\:\delta\:{and}\:{the}\:{density}\:{of}\:{the}\:{air}\:{is}\:\rho. \\ $$$${the}\:{mass}\:{of}\:{of}\:{the}\:{object}\:{is}\:{measured}\:{with}\:\:{the}\:{help}\:{of}\:{a}\:{metal}\:{weight}\:{of}\:{mass}\:{m}\:. \\ $$$${the}\:{density}\:{of}\:{the}\:{metal}\:{weight}\:{is}\:{d}. \\ $$$${if}\:\rho\ll\delta\:{them}\:{show}\:{that}\:{the}\:{real}\:{mass}\:{M}\:{will}\:{be} \\ $$$${m}\left(\mathrm{1}−\frac{\rho}{{d}}\:\right)\left(\mathrm{1}+\frac{\rho}{\delta}\right) \\ $$$${I}\:{have}\:{managed}\:{to}\:{M}=\frac{{m}\left(\mathrm{1}−\frac{\rho}{{d}}\right)}{\left(\mathrm{1}−\frac{\rho}{\delta}\right)} \\ $$$${but}\:{I}\:{can}\:{not}\:{figure}\:{it}\:{to}\:{the}\:{end} \\ $$$${please}\:{help} \\ $$

Question Number 220208 Answers: 3 Comments: 2

Question Number 220200 Answers: 0 Comments: 0

∫_1 ^( α) (((x − 1)^n )/(e^x − x − 1))dx

$$ \\ $$$$\int_{\mathrm{1}} ^{\:\alpha} \frac{\left({x}\:−\:\mathrm{1}\right)^{{n}} }{{e}^{{x}} \:−\:{x}\:−\:\mathrm{1}}{dx} \\ $$

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