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Question Number 37961 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^(2 ) +(√(1+x^2 )))) .

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}\:} \:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$

Question Number 37957 Answers: 0 Comments: 0

Question Number 37953 Answers: 0 Comments: 1

Question Number 37948 Answers: 0 Comments: 1

If x ∈R show that (2+i)e^((1+3i)) +(2−i)e^((1−3i)) is also real.

$${If}\:{x}\:\in\mathbb{R} \\ $$$${show}\:{that}\:\left(\mathrm{2}+{i}\right){e}^{\left(\mathrm{1}+\mathrm{3}{i}\right)} +\left(\mathrm{2}−{i}\right){e}^{\left(\mathrm{1}−\mathrm{3}{i}\right)} \:{is}\:{also}\:{real}. \\ $$

Question Number 37940 Answers: 1 Comments: 0

Which of the following expressions are positive for all real values of x? a) x^2 − 2x + 5 b) x^2 −2x−1 c) x^2 +4x+2 d) 2x^2 −6x + 5

$${Which}\:{of}\:{the}\:{following}\: \\ $$$${expressions}\:{are}\:{positive}\:{for} \\ $$$${all}\:{real}\:{values}\:{of}\:\:{x}? \\ $$$$\left.{a}\left.\right)\:{x}^{\mathrm{2}} −\:\mathrm{2}{x}\:+\:\mathrm{5}\:\:\:{b}\right)\:{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\: \\ $$$$\left.{c}\left.\right)\:{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:\:\:\:\:\:{d}\right)\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\:\mathrm{5} \\ $$

Question Number 37938 Answers: 5 Comments: 5

Question Number 37945 Answers: 0 Comments: 10

Two plane mirrors are inclined at an angle of 30°.A ray of light which makes an angle of incidence of 50° with one of the mirrors,undergoes two successive reflections at the mirrors.Calculate the angle of deviation. please help....its urgent

$${Two}\:{plane}\:{mirrors}\:{are}\:{inclined}\:{at} \\ $$$${an}\:{angle}\:{of}\:\mathrm{30}°.{A}\:{ray}\:{of}\:{light}\:{which} \\ $$$${makes}\:{an}\:{angle}\:{of}\:{incidence}\:{of}\:\mathrm{50}° \\ $$$${with}\:{one}\:{of}\:{the}\:{mirrors},{undergoes} \\ $$$${two}\:{successive}\:{reflections}\:{at}\:{the} \\ $$$${mirrors}.{Calculate}\:{the}\:{angle}\:{of} \\ $$$${deviation}. \\ $$$$ \\ $$$$ \\ $$$${please}\:{help}....{its}\:{urgent} \\ $$

Question Number 37930 Answers: 1 Comments: 1

n∈N U_(n+1) =((1/2))^(n+1) +U_n U_n =?

$${n}\in\mathbb{N} \\ $$$${U}_{{n}+\mathrm{1}} =\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{{n}+\mathrm{1}} +{U}_{{n}} \\ $$$${U}_{{n}} =? \\ $$

Question Number 37922 Answers: 1 Comments: 2

f : N → R g : N → R f(n)=∫_0 ^(2π) x^n sin x dx g(n)=∫_0 ^(2π) x^n cos x dx ((f(n+1)−f(n))/(g(n+1)−g(n)))=?

$${f}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${g}\::\:\mathbb{N}\:\rightarrow\:\mathbb{R} \\ $$$${f}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{sin}\:{x}\:{dx} \\ $$$${g}\left({n}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} {x}^{{n}} \mathrm{cos}\:{x}\:{dx} \\ $$$$\frac{{f}\left({n}+\mathrm{1}\right)−{f}\left({n}\right)}{{g}\left({n}+\mathrm{1}\right)−{g}\left({n}\right)}=? \\ $$

Question Number 37915 Answers: 1 Comments: 0

If y=4x^2 −1 , then find ((85)/(169))+Σ_(i=1) ^(84) (1/(y(i)))

$$\mathrm{If}\:{y}=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{85}}{\mathrm{169}}+\underset{{i}=\mathrm{1}} {\overset{\mathrm{84}} {\Sigma}}\:\frac{\mathrm{1}}{{y}\left({i}\right)}\: \\ $$

Question Number 37914 Answers: 1 Comments: 0

In △ABC, if sin A=sin^2 B then prove 4 cos 2A−4 cos 2B=1−cos 4B

$$\mathrm{In}\:\bigtriangleup{ABC},\:\mathrm{if}\:\mathrm{sin}\:\mathrm{A}=\mathrm{sin}^{\mathrm{2}} {B}\: \\ $$$$\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{4}\:\mathrm{cos}\:\mathrm{2}{A}−\mathrm{4}\:\mathrm{cos}\:\mathrm{2}{B}=\mathrm{1}−\mathrm{cos}\:\mathrm{4}{B} \\ $$

Question Number 37913 Answers: 1 Comments: 0

Solve the diferential equatuion (dy/dx)=((2x+y+1)/(x−2y+3))

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{diferential}\:\mathrm{equatuion} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{2}{x}+{y}+\mathrm{1}}{{x}−\mathrm{2}{y}+\mathrm{3}}\: \\ $$

Question Number 37912 Answers: 1 Comments: 1

Evaluate : the Integral ∫_(-(π/2)) ^(π/2) ∫_0 ^(3 cos θ) r^2 sin^2 θ. dr dθ

$$\mathrm{Evaluate}\::\:\mathrm{the}\:\mathrm{Integral} \\ $$$$\int_{-\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \int_{\mathrm{0}} ^{\mathrm{3}\:\mathrm{cos}\:\theta} {r}^{\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \theta.\:{dr}\:{d}\theta\: \\ $$

Question Number 37911 Answers: 0 Comments: 1

the function f(x) is defined by f(x) = { ((−x + 1 , for x≤3)),((kx − 8 , for x ≥ 3)) :} find the value of k .

$$\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\begin{cases}{−{x}\:+\:\mathrm{1}\:,\:{for}\:{x}\leqslant\mathrm{3}}\\{{kx}\:−\:\mathrm{8}\:,\:{for}\:{x}\:\geqslant\:\mathrm{3}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{k}\:. \\ $$

Question Number 37906 Answers: 1 Comments: 0

Question Number 37902 Answers: 2 Comments: 1

ind the value of f(a) =∫_0 ^(+∞) (dx/(x^2 +(√(a^2 +x^2 )))) dx witha>0 2)calculate f^′ (a) .

$${ind}\:{the}\:{value}\:{of}\:{f}\left({a}\right)\:\:=\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{2}} \:+\sqrt{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }}\:{dx} \\ $$$${witha}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{'} \left({a}\right)\:. \\ $$

Question Number 37901 Answers: 0 Comments: 1

let f(x)= (1+e^(−x) )^n 1) calculate f^((p)) (x) and f^((p)) (o) 2)calculate f^((n)) (0) 3)developp f at integr serie .

$${let}\:{f}\left({x}\right)=\:\left(\mathrm{1}+{e}^{−{x}} \right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({p}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({p}\right)} \left({o}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right){developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 37898 Answers: 1 Comments: 1

calculate f(λ) = ∫_0 ^(+∞) e^(−λx) cos(π[x])dx withλ>0

$${calculate}\:{f}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{+\infty} \:\:{e}^{−\lambda{x}} \:{cos}\left(\pi\left[{x}\right]\right){dx} \\ $$$${with}\lambda>\mathrm{0} \\ $$

Question Number 37896 Answers: 2 Comments: 1

let I_n = ∫_0 ^n (((−1)^([x]) )/((2x+1)^2 ))dx 1) calculate I_n interms of n 2) find lim_(n→+∞) I_n

$${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\frac{\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}_{{n}} \:\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{I}_{{n}} \\ $$

Question Number 37895 Answers: 1 Comments: 0

calculate A_n =∫_0 ^n (x−[(√x)])dx and lim_(n→+∞) A_n

$${calculate}\:\:\:{A}_{{n}} =\int_{\mathrm{0}} ^{{n}} \left({x}−\left[\sqrt{{x}}\right]\right){dx}\:{and} \\ $$$${lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \\ $$

Question Number 37894 Answers: 0 Comments: 0

find nature of the serie Σ_(n=1) ^∞ (Σ_(k=0) ^n (1/C_n ^k ))x^n

$${find}\:{nature}\:{of}\:{the}\:{serie} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\left(\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{{C}_{{n}} ^{{k}} }\right){x}^{{n}} \\ $$

Question Number 37893 Answers: 1 Comments: 1

calculate ∫_0 ^1 (√(x+(√(x+1)))) dx .

$${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}+\sqrt{{x}+\mathrm{1}}}\:{dx}\:. \\ $$

Question Number 37892 Answers: 0 Comments: 3

let f(x)=(√(x+(√(x+1)))) 1) find D_f 2) give the equation of assymtote at point A(0,f(o)) 3) if f(x)∼ a(x−1) +b (x→1) determine a andb 4) calculate f^′ (x) 5) find f^(−1) (x) and (f^(−1) )^′ (x)

$${let}\:\:\:{f}\left({x}\right)=\sqrt{{x}+\sqrt{{x}+\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:\:{give}\:{the}\:{equation}\:{of}\:{assymtote}\:{at}\:{point} \\ $$$${A}\left(\mathrm{0},{f}\left({o}\right)\right) \\ $$$$\left.\mathrm{3}\right)\:{if}\:{f}\left({x}\right)\sim\:{a}\left({x}−\mathrm{1}\right)\:\:+{b}\:\:\left({x}\rightarrow\mathrm{1}\right)\:{determine}\:{a}\:{andb} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{5}\right)\:{find}\:\:{f}^{−\mathrm{1}} \left({x}\right)\:\:{and}\:\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right) \\ $$

Question Number 37891 Answers: 0 Comments: 1

calculate B_n = Σ_(k=0) ^n (−1)^k (2k^2 +1) interms of n.

$${calculate}\:{B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(−\mathrm{1}\right)^{{k}} \left(\mathrm{2}{k}^{\mathrm{2}} \:+\mathrm{1}\right)\:{interms}\:{of}\:{n}. \\ $$

Question Number 37890 Answers: 0 Comments: 2

calculate A_n = Σ_(k=0) ^n (−1)^k (2k+3) interms of n

$${calculate}\:{A}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(−\mathrm{1}\right)^{{k}} \left(\mathrm{2}{k}+\mathrm{3}\right)\:{interms}\:{of}\:{n} \\ $$

Question Number 37889 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(2x))/x) e^(−tx) dx with t ≥0

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}}\:{e}^{−{tx}} \:{dx}\:{with}\:{t}\:\geqslant\mathrm{0} \\ $$

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