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Question Number 97506    Answers: 0   Comments: 0

please prove it cos x= J_0 (x) + 2Σ_(x−1) (−1)^x J_(2n) (x)

$${please}\:{prove}\:{it} \\ $$$$ \\ $$$$\mathrm{cos}\:{x}=\:{J}_{\mathrm{0}} \left({x}\right)\:+\:\mathrm{2}\sum_{{x}−\mathrm{1}} \left(−\mathrm{1}\right)^{{x}} {J}_{\mathrm{2}{n}} \left({x}\right) \\ $$

Question Number 97501    Answers: 0   Comments: 2

The natural number n for which the expression y = 5log^2 _3 (n) − log _3 (n^(12) )+9 , has the minimum value is ___

$$\mathrm{The}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{the}\:\mathrm{expression}\:\mathrm{y}\:=\:\mathrm{5log}^{\mathrm{2}} \:_{\mathrm{3}} \left(\mathrm{n}\right)\:− \\ $$$$\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{n}^{\mathrm{12}} \right)+\mathrm{9}\:,\:\mathrm{has}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 97505    Answers: 0   Comments: 0

Question Number 97497    Answers: 2   Comments: 0

Question Number 97496    Answers: 1   Comments: 0

if f(((2x+5)/(x−3)))=3x+5 find f(x) please solve it

$${if}\:\:\:\:\:\:{f}\left(\frac{\mathrm{2}{x}+\mathrm{5}}{{x}−\mathrm{3}}\right)=\mathrm{3}{x}+\mathrm{5}\:\:\:{find}\:\:\:{f}\left({x}\right) \\ $$$$ \\ $$$${please}\:{solve}\:{it} \\ $$

Question Number 97494    Answers: 1   Comments: 0

Question Number 97492    Answers: 2   Comments: 0

Question Number 97490    Answers: 1   Comments: 0

please prove it cosx= J_0 (x)+2Σ_(x−1) (−1)^x J_(2x) (x)

$${please}\:\:{prove}\:\:{it} \\ $$$$\mathrm{cos}{x}=\:{J}_{\mathrm{0}} \left({x}\right)+\mathrm{2}\sum_{{x}−\mathrm{1}} \left(−\mathrm{1}\right)^{{x}} {J}_{\mathrm{2}{x}} \left({x}\right) \\ $$

Question Number 97489    Answers: 2   Comments: 0

please prove it ∫_0 ^∞ e^(−ax^2 ) cos bx dx= (1/2)(√(π/a)).e^(−(b^2 /(4a)))

$${please}\:\:{prove}\:{it} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} {e}^{−{ax}^{\mathrm{2}} } \mathrm{cos}\:{bx}\:\:{dx}=\:\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\frac{\pi}{{a}}}.{e}^{−\frac{{b}^{\mathrm{2}} }{\mathrm{4}{a}}} \\ $$

Question Number 97485    Answers: 1   Comments: 3

Question Number 97483    Answers: 1   Comments: 4

In each week the growth of a plant is two−thirds the growth of the previous week. The plant grows 12 cm in the first week. (a) Calculate the growth of the plant in (b) the limiting height of the pant

$$\mathrm{In}\:\mathrm{each}\:\mathrm{week}\:\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{a}\:\mathrm{plant}\:\mathrm{is}\:\mathrm{two}−\mathrm{thirds} \\ $$$$\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{previous}\:\mathrm{week}. \\ $$$$\mathrm{The}\:\mathrm{plant}\:\mathrm{grows}\:\mathrm{12}\:\mathrm{cm}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{week}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{growth}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plant}\:\mathrm{in}\: \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{limiting}\:\mathrm{height}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pant} \\ $$

Question Number 97479    Answers: 2   Comments: 2

Question Number 97478    Answers: 0   Comments: 0

Find the global parametrization of the curve { x^2 +y^2 +z^2 =1; x+y−z=0 }

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{global}\:\mathrm{parametrization} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\left\{\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} =\mathrm{1};\:\mathrm{x}+\mathrm{y}−\mathrm{z}=\mathrm{0}\:\right\}\: \\ $$

Question Number 97476    Answers: 0   Comments: 0

2F1((1/2),(1/2);(1/2);z)=(1−z)^(1/2) ∗∗1 by kummer transformation 2F1((1/2),(1/2);(1/2);z)=2F1((1/2),(1/2);1+(1/2)+(1/2)−(1/2);z) 2F1((1/2),(1/2);(1/2);z)=((sin^(−1) (√(1−z)))/(√(1−z)))∗∗2 why do i get different answer in ∗∗1 and 2∗∗

$$\mathrm{2}{F}\mathrm{1}\left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{1}}{\mathrm{2}};{z}\right)=\left(\mathrm{1}−{z}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \ast\ast\mathrm{1} \\ $$$${by}\:{kummer}\:{transformation} \\ $$$$\mathrm{2}{F}\mathrm{1}\left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{1}}{\mathrm{2}};{z}\right)=\mathrm{2}{F}\mathrm{1}\left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}};{z}\right) \\ $$$$\mathrm{2}{F}\mathrm{1}\left(\frac{\mathrm{1}}{\mathrm{2}},\frac{\mathrm{1}}{\mathrm{2}};\frac{\mathrm{1}}{\mathrm{2}};{z}\right)=\frac{{sin}^{−\mathrm{1}} \sqrt{\mathrm{1}−{z}}}{\sqrt{\mathrm{1}−{z}}}\ast\ast\mathrm{2} \\ $$$$ \\ $$$${why}\:{do}\:{i}\:{get}\:{different}\:{answer}\:{in} \\ $$$$\ast\ast\mathrm{1}\:{and}\:\mathrm{2}\ast\ast \\ $$

Question Number 97465    Answers: 2   Comments: 1

∫_0 ^∝ e^(−x^4 ) dx=(1/4) please prove it

$$\int_{\mathrm{0}} ^{\propto} {e}^{−{x}^{\mathrm{4}} } {dx}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$${please}\:{prove}\:{it} \\ $$

Question Number 97463    Answers: 0   Comments: 2

Question Number 97462    Answers: 0   Comments: 1

Question Number 97460    Answers: 1   Comments: 2

Question Number 97454    Answers: 2   Comments: 0

Question Number 97439    Answers: 0   Comments: 2

∫_((√2)/2) ^1 ((x^3 /2) + (1/(6x)))(√(1+(((3x^2 )/2) −(1/(6x^2 )))^2 )) dx

$$\underset{\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}\:\left(\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{6x}}\right)\sqrt{\mathrm{1}+\left(\frac{\mathrm{3x}^{\mathrm{2}} }{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{6x}^{\mathrm{2}} }\right)^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 97438    Answers: 1   Comments: 1

If −3≤x≤4, −2≤y≤5, 4≤z≤10 , find the greatest value of w = z−xy

$$\mathrm{If}\:−\mathrm{3}\leqslant\mathrm{x}\leqslant\mathrm{4},\:−\mathrm{2}\leqslant\mathrm{y}\leqslant\mathrm{5},\:\mathrm{4}\leqslant\mathrm{z}\leqslant\mathrm{10} \\ $$$$,\:\mathrm{find}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{w}\:=\:\mathrm{z}−\mathrm{xy}\: \\ $$

Question Number 97423    Answers: 2   Comments: 0

solve y^(′′) +4y =xe^(−x) with y(0)=1 and y^′ (0) =−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{4y}\:=\mathrm{xe}^{−\mathrm{x}} \:\:\:\:\mathrm{with}\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=−\mathrm{1} \\ $$

Question Number 97428    Answers: 2   Comments: 5

Question Number 97418    Answers: 1   Comments: 1

Verify if the series Σ_(n=1) ^n ((2n + 5)/(n^2 +3n + 2)) is convergent or divergent. What method is easier?

$$\mathrm{Verify}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\: \\ $$$$\:\underset{{n}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{2}{n}\:+\:\mathrm{5}}{{n}^{\mathrm{2}} \:+\mathrm{3}{n}\:+\:\mathrm{2}}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}. \\ $$$$\mathrm{What}\:\mathrm{method}\:\mathrm{is}\:\mathrm{easier}? \\ $$

Question Number 97417    Answers: 1   Comments: 0

∫(x/(a+sin^2 x))dx=?

$$\int\frac{{x}}{{a}+\mathrm{sin}^{\mathrm{2}} \:{x}}{dx}=? \\ $$

Question Number 97413    Answers: 1   Comments: 0

Given that ω = e^(iθ) , θ≠ nπ , n ∈N show that (1 + ω)^n = 2^n ((1/2)θ)e^((1/2)(inθ)) please help me out on this, i′ve stumbled on it.

$$\mathrm{Given}\:\mathrm{that}\:\omega\:=\:{e}^{{i}\theta} ,\:\theta\neq\:{n}\pi\:,\:{n}\:\in\mathbb{N} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{1}\:+\:\omega\right)^{{n}} \:=\:\mathrm{2}^{{n}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right){e}^{\frac{\mathrm{1}}{\mathrm{2}}\left({in}\theta\right)} \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out}\:\mathrm{on}\:\mathrm{this},\:\mathrm{i}'\mathrm{ve}\:\mathrm{stumbled}\:\mathrm{on}\:\mathrm{it}. \\ $$

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