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Question Number 42087 Answers: 0 Comments: 0

find ∫ ((x dx)/(x(√(1+x^2 )) +(1+x^2 )(√x)))

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

Question Number 42086 Answers: 1 Comments: 0

let f(x) =∫_0 ^2 ((ch(t))/(2xsh(t) +1)) dt 1) find a simple form of f(x) 2) calculate ∫_0 ^2 ((ch(t))/(1+sh(t)))dt 3) calculate ∫_0 ^2 ((ch(t))/(3sh(t) +1))dt .

$${let}\:\:\:\:{f}\left({x}\right)\:\:=\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{2}{xsh}\left({t}\right)\:+\mathrm{1}}\:{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{1}+{sh}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\:\:\frac{{ch}\left({t}\right)}{\mathrm{3}{sh}\left({t}\right)\:+\mathrm{1}}{dt}\:. \\ $$

Question Number 42085 Answers: 1 Comments: 1

calculate ∫_1 ^(+∞) ((2x+1)/(3 +(x+1)^3 ))dx

$${calculate}\:\:\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\mathrm{3}\:+\left({x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\: \\ $$

Question Number 42083 Answers: 0 Comments: 0

calculate ∫_0 ^1 ((2x+1)/(3+(1+x)^3 ))dx

$${calculate}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\:\:\frac{\mathrm{2}{x}+\mathrm{1}}{\mathrm{3}+\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }{dx} \\ $$

Question Number 42058 Answers: 1 Comments: 0

Given that x^ = ((Σxi)/n_1 ) and y^ = ((Σyi)/n_2 ) show that x_c ^ = ((n_1 (x^ ) + n_2 (y^ ))/(n_1 +n_2 ))

$${Given}\:{that}\:\:\bar {\mathrm{x}}=\:\frac{\Sigma\mathrm{x}{i}}{{n}_{\mathrm{1}} }\:\:\:{and}\:\bar {{y}}=\:\frac{\Sigma{yi}}{{n}_{\mathrm{2}} } \\ $$$${show}\:{that}\: \\ $$$$\:\bar {\mathrm{x}}_{{c}} =\:\frac{{n}_{\mathrm{1}} \left(\bar {\mathrm{x}}\right)\:+\:{n}_{\mathrm{2}} \left(\bar {{y}}\right)}{{n}_{\mathrm{1}} +{n}_{\mathrm{2}} } \\ $$

Question Number 42054 Answers: 1 Comments: 1

Question Number 42093 Answers: 1 Comments: 0

If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, then the rank of the permutation debac is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{permutations}\:\mathrm{of}\:{a},\:{b},\:{c},\:{d},\:{e}\:\mathrm{taken} \\ $$$$\mathrm{all}\:\mathrm{together}\:\mathrm{be}\:\mathrm{written}\:\mathrm{down}\:\mathrm{in}\: \\ $$$$\mathrm{alphabetical}\:\mathrm{order}\:\mathrm{as}\:\mathrm{in}\:\mathrm{dictionary} \\ $$$$\mathrm{and}\:\mathrm{numbered},\:\mathrm{then}\:\mathrm{the}\:\mathrm{rank}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{permutation}\:\:{debac}\:\:\mathrm{is} \\ $$

Question Number 42045 Answers: 0 Comments: 2

i have some thing to say...in this platform several people/students/others post questions..others take promt action to solve the problems.. after the problem got solved..the person/students who post questions never attend or see the answer even do not clarify whether the answer is right or wrong...or whether he/she got understood the method...so pls show your courtsey otherwise your problem remain a problem and nobody bother to solve it...Than you all

$${i}\:{have}\:{some}\:{thing}\:{to}\:{say}...{in}\:{this}\:{platform}\:\:{several} \\ $$$${people}/{students}/{others}\:{post}\:{questions}..{others} \\ $$$${take}\:{promt}\:{action}\:{to}\:{solve}\:{the}\:{problems}.. \\ $$$${after}\:{the}\:{problem}\:{got}\:{solved}..{the}\:{person}/{students} \\ $$$${who}\:{post}\:{questions}\:{never}\:{attend}\:{or}\:{see}\:{the}\:{answer} \\ $$$${even}\:{do}\:{not}\:{clarify}\:{whether}\:{the}\:{answer}\:{is}\:{right} \\ $$$${or}\:{wrong}...{or}\:{whether}\:{he}/{she}\:{got}\:{understood}\:{the} \\ $$$${method}...{so}\:{pls}\:{show}\:{your}\:{courtsey}\:{otherwise} \\ $$$${your}\:{problem}\:{remain}\:{a}\:{problem}\:{and}\:{nobody}\:{bother} \\ $$$${to}\:{solve}\:{it}...{Than}\:{you}\:{all} \\ $$

Question Number 42036 Answers: 0 Comments: 13

State the phase shift, the amplitude and draw the graph. (a) g(θ) = (3/4) sin(2θ + π) (b) f(θ) = 1 + (3/4) sin(2θ + π) (c) f(θ) = 4θ

$$\mathrm{State}\:\mathrm{the}\:\mathrm{phase}\:\mathrm{shift},\:\:\mathrm{the}\:\mathrm{amplitude}\:\mathrm{and}\:\mathrm{draw}\:\mathrm{the}\:\mathrm{graph}. \\ $$$$\left(\mathrm{a}\right)\:\:\mathrm{g}\left(\theta\right)\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\left(\mathrm{2}\theta\:+\:\pi\right) \\ $$$$\left(\mathrm{b}\right)\:\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{1}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\left(\mathrm{2}\theta\:+\:\pi\right) \\ $$$$\left(\mathrm{c}\right)\:\:\mathrm{f}\left(\theta\right)\:=\:\mathrm{4}\theta \\ $$$$ \\ $$

Question Number 42030 Answers: 4 Comments: 1

x+(1/x)=5 x^5 +(1/x^5 )=?

$$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{5}\:\:\:\:\mathrm{x}^{\mathrm{5}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{5}} }=? \\ $$

Question Number 42029 Answers: 1 Comments: 0

Question Number 42025 Answers: 0 Comments: 2

A man,near point is 90cm from his eyes and his far point is 3cm. What type of eye defect has he? If he is to read a book at 25cm and see distant object clearly,what type and power of lenses will you recommend for him?

$${A}\:{man},{near}\:{point}\:{is}\:\mathrm{90}{cm}\:{from} \\ $$$${his}\:{eyes}\:{and}\:{his}\:{far}\:{point}\:{is}\:\mathrm{3}{cm}. \\ $$$${What}\:{type}\:{of}\:{eye}\:{defect}\:{has}\:{he}? \\ $$$${If}\:{he}\:{is}\:{to}\:{read}\:{a}\:{book}\:{at}\:\mathrm{25}{cm}\:{and} \\ $$$${see}\:{distant}\:{object}\:{clearly},{what}\:{type} \\ $$$${and}\:{power}\:{of}\:{lenses}\:{will}\:{you} \\ $$$${recommend}\:{for}\:{him}? \\ $$$$ \\ $$

Question Number 42020 Answers: 0 Comments: 0

let S_n (x)=Σ_(k=1) ^n (x^k /(√k)) find a equivalent of S_n (x) when n→+∞

$${let}\:\:{S}_{{n}} \left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{x}^{{k}} }{\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \left({x}\right)\:{when}\:{n}\rightarrow+\infty \\ $$

Question Number 42019 Answers: 1 Comments: 3

find x: 2^x + 3^x = 13

$$\mathrm{find}\:\mathrm{x}:\:\:\:\:\:\mathrm{2}^{\mathrm{x}} \:+\:\mathrm{3}^{\mathrm{x}} \:=\:\mathrm{13} \\ $$

Question Number 42012 Answers: 2 Comments: 0

Solve : (du/dt) = ((3u−7t)/(−7u+3t))

$$\mathrm{Solve}\:: \\ $$$$\frac{{d}\mathrm{u}}{{d}\mathrm{t}}\:=\:\frac{\mathrm{3u}−\mathrm{7t}}{−\mathrm{7u}+\mathrm{3t}} \\ $$

Question Number 42009 Answers: 1 Comments: 0

if (a+bω+cω^2 )+(aω+bω^2 +c)^2 +(aω^2 +b+cω)^2 =0 then prove that a=c or a+c=2b

$$\mathrm{if}\:\left(\mathrm{a}+\mathrm{b}\omega+\mathrm{c}\omega^{\mathrm{2}} \right)+\left(\mathrm{a}\omega+\mathrm{b}\omega^{\mathrm{2}} +\mathrm{c}\right)^{\mathrm{2}} +\left(\mathrm{a}\omega^{\mathrm{2}} +\mathrm{b}+\mathrm{c}\omega\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{a}=\mathrm{c}\:\:\mathrm{or}\:\:\:\mathrm{a}+\mathrm{c}=\mathrm{2b} \\ $$

Question Number 42007 Answers: 2 Comments: 0

Question Number 41998 Answers: 1 Comments: 0

lim_(x→∞) ((x + cos x)/(x + sin x))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}\:+\:\mathrm{cos}\:{x}}{{x}\:+\:\mathrm{sin}\:{x}} \\ $$

Question Number 41989 Answers: 2 Comments: 1

Question Number 41985 Answers: 1 Comments: 1

Prove e^x ≥x+1 ∀x∈R in as many ways as you can show

$$\mathrm{Prove}\:{e}^{{x}} \geqslant{x}+\mathrm{1}\:\forall{x}\in\mathbb{R}\:\mathrm{in}\:\mathrm{as}\:\mathrm{many}\:\mathrm{ways} \\ $$$$\mathrm{as}\:\mathrm{you}\:\mathrm{can}\:\mathrm{show} \\ $$

Question Number 41984 Answers: 2 Comments: 7

solve simultaneously: 2(√k) + h = 9 ....... (i) k + 2(√h) = 3 ....... (ii)

$$\mathrm{solve}\:\mathrm{simultaneously}:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\sqrt{\mathrm{k}}\:\:+\:\mathrm{h}\:=\:\mathrm{9}\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{k}\:+\:\mathrm{2}\sqrt{\mathrm{h}}\:\:=\:\mathrm{3}\:\:.......\:\left(\mathrm{ii}\right) \\ $$

Question Number 41966 Answers: 1 Comments: 0

Question Number 41964 Answers: 1 Comments: 10

Prof Kintush has a near point of 45cm and his far point is infinity. What type of lens and focal length should be recommended for his normal reading?

$${Prof}\:{Kintush}\:{has}\:{a}\:{near}\:{point}\:{of} \\ $$$$\mathrm{45}{cm}\:{and}\:{his}\:{far}\:{point}\:{is}\:{infinity}. \\ $$$${What}\:{type}\:{of}\:{lens}\:{and}\:{focal}\:{length} \\ $$$${should}\:{be}\:{recommended}\:{for}\:{his} \\ $$$${normal}\:{reading}? \\ $$

Question Number 41958 Answers: 1 Comments: 0

{ ((x^(√y) +y^(√x) =((49)/(48)))),(((√x)+(√y)=(7/2))) :} find x and y k.k

$$\begin{cases}{\mathrm{x}^{\sqrt{\mathrm{y}}} +\mathrm{y}^{\sqrt{\mathrm{x}}} =\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{k}.\mathrm{k} \\ $$

Question Number 41957 Answers: 1 Comments: 1

Question Number 41913 Answers: 1 Comments: 0

let f(a) = ∫_0 ^π (x/(1+acosx))dx 1) find f(a) 2) calculate ∫_0 ^π (x/(1+2cosx))dx and ∫_0 ^π (x/(1−2cosx))dx 3) calculate ∫_0 ^π ((xcosx)/((1+acosx)^2 ))dx 4) find the value of ∫_0 ^π ((xcosx)/((1+2cosx)^2 ))dx .

$${let}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}}{\mathrm{1}+{acosx}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{f}\left({a}\right)\: \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}}{\mathrm{1}+\mathrm{2}{cosx}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{x}}{\mathrm{1}−\mathrm{2}{cosx}}{dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xcosx}}{\left(\mathrm{1}+{acosx}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xcosx}}{\left(\mathrm{1}+\mathrm{2}{cosx}\right)^{\mathrm{2}} }{dx}\:. \\ $$

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