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Question Number 91678    Answers: 0   Comments: 0

(y+2px)^2 = 2px^2 solve by Clairaut′s method

$$\left({y}+\mathrm{2}{px}\right)^{\mathrm{2}} \:=\:\mathrm{2}{px}^{\mathrm{2}} \\ $$$${solve}\:{by}\:{Clairaut}'{s}\:{method}\: \\ $$

Question Number 91668    Answers: 0   Comments: 0

∫e^x^2 erf(x) dx

$$\int{e}^{{x}^{\mathrm{2}} } \:{erf}\left({x}\right)\:{dx} \\ $$

Question Number 91667    Answers: 0   Comments: 6

find the limits of 1. u_n =Σ_(k=1) ^n (n/(n^2 +k^2 )) 2. v_n =Σ_(k=1) ^n (1/(√(n^2 +2kn)))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{of}\: \\ $$$$\mathrm{1}.\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} }\:\:\: \\ $$$$\mathrm{2}.\:\mathrm{v}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$

Question Number 91660    Answers: 0   Comments: 4

Question Number 91656    Answers: 1   Comments: 2

Question Number 91655    Answers: 2   Comments: 12

A particle is projected with an intial velocity of u ms^(−1) at an angle α to the ground from a point O on the ground. Given that it clears two walls of hieght h and distances 2h and 4h respectively from O. (a) find the tangent of α (b) the maximum hieght (c) the range and period of the particle (d) show that u^2 = (4/(26)) gh please sir can you help me using the actual equations of projectile motion?

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{with}\:\mathrm{an}\:\mathrm{intial}\:\mathrm{velocity}\:\mathrm{of}\:{u}\:\mathrm{ms}^{−\mathrm{1}} \:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{to}\: \\ $$$$\mathrm{the}\:\mathrm{ground}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{O}\:\mathrm{on}\:\mathrm{the}\:\mathrm{ground}.\:\mathrm{Given}\:\mathrm{that}\:\mathrm{it}\:\mathrm{clears} \\ $$$$\mathrm{two}\:\mathrm{walls}\:\mathrm{of}\:\mathrm{hieght}\:{h}\:\mathrm{and}\:\mathrm{distances}\:\mathrm{2h}\:\mathrm{and}\:\mathrm{4h}\:\mathrm{respectively}\:\mathrm{from}\:\mathrm{O}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{of}\:\alpha \\ $$$$\left(\mathrm{b}\right)\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{hieght} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{the}\:\mathrm{range}\:\mathrm{and}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{show}\:\mathrm{that}\:{u}^{\mathrm{2}} \:=\:\frac{\mathrm{4}}{\mathrm{26}}\:\mathrm{g}{h}\: \\ $$$$\mathrm{please}\:\mathrm{sir}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{using}\:\mathrm{the}\:\mathrm{actual}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{projectile}\:\mathrm{motion}? \\ $$$$ \\ $$

Question Number 91654    Answers: 1   Comments: 0

th position vector of a particle p of mass 3 kg is given by r = [(cos 2t) i + (sin 2t)j] m given that p was intitialy at rest. find the cartesian equation of its path and describe it.

$$\mathrm{th}\:\mathrm{position}\:\mathrm{vector}\:\mathrm{of}\:\mathrm{a}\:\mathrm{particle}\:{p}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{3}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:{r}\:=\:\left[\left(\mathrm{cos}\:\mathrm{2}{t}\right)\:{i}\:+\:\left(\mathrm{sin}\:\mathrm{2}{t}\right){j}\right]\:\mathrm{m} \\ $$$$\mathrm{given}\:\mathrm{that}\:{p}\:\:\mathrm{was}\:\mathrm{intitialy}\:\mathrm{at}\:\mathrm{rest}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{cartesian}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{its}\:\mathrm{path}\:\mathrm{and}\:\mathrm{describe}\:\mathrm{it}. \\ $$

Question Number 91683    Answers: 0   Comments: 1

Question Number 91647    Answers: 1   Comments: 0

solve x⌊x⌊x⌊x⌋⌋⌋=2020

$${solve} \\ $$$${x}\lfloor{x}\lfloor{x}\lfloor{x}\rfloor\rfloor\rfloor=\mathrm{2020} \\ $$

Question Number 91643    Answers: 0   Comments: 4

(dy/dx) = ((y−x)/x)

$$\frac{{dy}}{{dx}}\:=\:\frac{{y}−{x}}{{x}}\: \\ $$$$ \\ $$

Question Number 91641    Answers: 0   Comments: 0

find ∫ ((cos^4 x+sin^4 x)/(cos^3 x+sin^3 x))dx

$${find}\:\int\:\frac{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}}{{cos}^{\mathrm{3}} {x}+{sin}^{\mathrm{3}} {x}}{dx} \\ $$

Question Number 91640    Answers: 0   Comments: 1

find nature of the serie Σ_n cos(πn^2 ln(1+(1/n)))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}} \:{cos}\left(\pi{n}^{\mathrm{2}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right) \\ $$

Question Number 91639    Answers: 0   Comments: 1

find lim_(n→∞) (1+(1/n))^2 ((n!)/n^(n+(1/2)) )

$${find}\:{lim}_{{n}\rightarrow\infty} \:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} \:\frac{{n}!}{{n}^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} } \\ $$

Question Number 91638    Answers: 1   Comments: 0

Find the general term: Σ_(n=1) ^k n^n

$${Find}\:{the}\:{general}\:{term}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}{n}^{{n}} \\ $$

Question Number 91637    Answers: 0   Comments: 0

f continue on [0,1] stady the serie Σ u_n with u_n =(−1)^n ∫_0 ^1 t^n f)t)dt

$${f}\:{continue}\:{on}\:\left[\mathrm{0},\mathrm{1}\right]\:{stady}\:{the}\:{serie}\:\Sigma\:{u}_{{n}} \:\:\:{with} \\ $$$$\left.{u}_{{n}} \left.=\left(−\mathrm{1}\right)^{{n}} \:\int_{\mathrm{0}} ^{\mathrm{1}} \:{t}^{{n}} {f}\right){t}\right){dt} \\ $$

Question Number 91636    Answers: 0   Comments: 0

∫(dx/(x((√x)+^5 (√x^2 ))))

$$\int\frac{{dx}}{{x}\left(\sqrt{{x}}+^{\mathrm{5}} \sqrt{{x}^{\mathrm{2}} }\right)} \\ $$

Question Number 91635    Answers: 0   Comments: 2

given f(x)=log_(10) (x) and log_(10) (102)≈2.0086 , which is closest to f ′(100)? A. 0.0043 B.0.0086 C. 0.01 E. 1.0043

$${given}\:{f}\left({x}\right)=\mathrm{log}_{\mathrm{10}} \left({x}\right)\:{and}\:\mathrm{log}_{\mathrm{10}} \left(\mathrm{102}\right)\approx\mathrm{2}.\mathrm{0086} \\ $$$$,\:{which}\:{is}\:{closest}\:{to}\:{f}\:'\left(\mathrm{100}\right)? \\ $$$${A}.\:\mathrm{0}.\mathrm{0043}\:\:\:\:\:\:{B}.\mathrm{0}.\mathrm{0086} \\ $$$${C}.\:\mathrm{0}.\mathrm{01}\:\:\:\:\:\:\:\:\:\:{E}.\:\mathrm{1}.\mathrm{0043} \\ $$

Question Number 91632    Answers: 0   Comments: 1

find a equivalent of U_n =1+(1/(√2))+(1/(√3))+...+(1/(√n))

$${find}\:{a}\:{equivalent}\:{of}\:{U}_{{n}} \:=\mathrm{1}+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}+...+\frac{\mathrm{1}}{\sqrt{{n}}} \\ $$

Question Number 91631    Answers: 0   Comments: 1

find a equivalent of Σ_(k=2) ^n ln(k)

$${find}\:{a}\:{equivalent}\:{of}\:\sum_{{k}=\mathrm{2}} ^{{n}} {ln}\left({k}\right) \\ $$

Question Number 91630    Answers: 0   Comments: 1

show that ∫_(−(π/4)) ^(π/4) ((sin2x)/((2+cos2x)^2 ))ln(1+e^x )dx =(π/(16))−((π(√3))/(36))

$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{sin2x}}{\left(\mathrm{2}+\mathrm{cos2x}\right)^{\mathrm{2}} }\mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$$$=\frac{\pi}{\mathrm{16}}−\frac{\pi\sqrt{\mathrm{3}}}{\mathrm{36}} \\ $$

Question Number 91624    Answers: 0   Comments: 4

Question Number 91622    Answers: 2   Comments: 1

((d(x!))/dx)=

$$\frac{\mathrm{d}\left(\mathrm{x}!\right)}{\mathrm{dx}}= \\ $$

Question Number 91621    Answers: 0   Comments: 1

calculate ∫_0 ^∞ sin(x^6 )dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{6}} \right){dx} \\ $$

Question Number 91620    Answers: 0   Comments: 1

let f(x) =2 x−(√(x−1)) find ∫ ((f(x))/(f^(−1) (x)))dx and ∫ ln(((f(x))/(f^(−1) (x))))dx

$${let}\:{f}\left({x}\right)\:=\mathrm{2}\:{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\int\:\:\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}{dx}\:\:{and}\:\:\int\:{ln}\left(\frac{{f}\left({x}\right)}{{f}^{−\mathrm{1}} \left({x}\right)}\right){dx} \\ $$

Question Number 91619    Answers: 0   Comments: 1

calculate ∫_2 ^(+∞) (((−1)^([2x]) )/(x[x]−1))dx

$${calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\left[\mathrm{2}{x}\right]} }{{x}\left[{x}\right]−\mathrm{1}}{dx} \\ $$

Question Number 91615    Answers: 0   Comments: 2

hi every one is it right if we use tylor in this integration and if there were another way that will be very cool ∫sin(x^4 )dx

$${hi}\:{every}\:{one}\:{is}\:{it}\:{right}\:{if}\:{we}\:{use}\:{tylor} \\ $$$${in}\:{this}\:{integration}\:{and}\:{if}\:{there}\:{were} \\ $$$${another}\:{way}\:{that}\:{will}\:{be}\:{very}\:{cool} \\ $$$$\int{sin}\left({x}^{\mathrm{4}} \right){dx}\: \\ $$$$ \\ $$$$ \\ $$

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