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Question Number 121315    Answers: 2   Comments: 0

find lim ∫_(1/n) ^n arctan(1+(x/n))e^(−nx) dx

$${find}\:{lim}\:\int_{\frac{\mathrm{1}}{{n}}} ^{{n}} {arctan}\left(\mathrm{1}+\frac{{x}}{{n}}\right){e}^{−{nx}} {dx} \\ $$

Question Number 121314    Answers: 1   Comments: 0

find lim_(n→+∞) ∫_0 ^n ((cos(nx))/(x^2 +n^2 ))dx

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{cos}\left({nx}\right)}{{x}^{\mathrm{2}} +{n}^{\mathrm{2}} }{dx} \\ $$

Question Number 121303    Answers: 1   Comments: 1

cos x − (√3) sin x = 2 cos 2x

$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\: \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:{x}\:−\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:\mathrm{cos}\:\mathrm{2}{x} \\ $$$$\: \\ $$$$\: \\ $$

Question Number 121302    Answers: 2   Comments: 0

(1)lim_(x→0) (((1−e^(2x) )sin (3x))/(∣4x∣)) ? (2) lim_(x→0) ⌊ (((1−e^(2x) )sin 3x)/(∣4x∣)) ⌋ ?

$$\:\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}−\mathrm{e}^{\mathrm{2x}} \right)\mathrm{sin}\:\left(\mathrm{3x}\right)}{\mid\mathrm{4x}\mid}\:?\: \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\lfloor\:\frac{\left(\mathrm{1}−\mathrm{e}^{\mathrm{2x}} \right)\mathrm{sin}\:\mathrm{3x}}{\mid\mathrm{4x}\mid}\:\rfloor\:? \\ $$

Question Number 121301    Answers: 1   Comments: 0

Question Number 121300    Answers: 2   Comments: 1

∫ (dx/(x^3 +x^2 +x+1)) ?

$$\:\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:? \\ $$

Question Number 121330    Answers: 1   Comments: 2

Question Number 121293    Answers: 1   Comments: 6

give me difficult problems exponent

$$\mathrm{give}\:\mathrm{me}\:\mathrm{difficult}\:\mathrm{problems}\:\mathrm{exponent}\: \\ $$

Question Number 121282    Answers: 1   Comments: 0

... advanced mathematics... prove that :: Ψ=∫_0 ^( 1) Γ(2−x)Γ(1+x)dx=(7/π^2 ) ζ(3) ...m.n.july.1970...

$$\:\:\:\:\:\:\:\:...\:\mathrm{advanced}\:\:\mathrm{mathematics}... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Psi=\int_{\mathrm{0}} ^{\:\mathrm{1}} \Gamma\left(\mathrm{2}−{x}\right)\Gamma\left(\mathrm{1}+{x}\right){dx}=\frac{\mathrm{7}}{\pi^{\mathrm{2}} }\:\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\mathrm{m}.\mathrm{n}.\mathrm{july}.\mathrm{1970}... \\ $$$$ \\ $$

Question Number 121278    Answers: 1   Comments: 0

The domaine of the function f(x)=((√(log_(0.5) (x^2 −7x+13))))^(−1) is;

$$\mathrm{The}\:\mathrm{domaine}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left(\sqrt{\mathrm{log}_{\mathrm{0}.\mathrm{5}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{7x}+\mathrm{13}\right)}\right)^{−\mathrm{1}} \:\mathrm{is}; \\ $$

Question Number 121264    Answers: 2   Comments: 0

Find the point on the curve x=2y^2 closest to the point (10,0)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the}\:\mathrm{curve} \\ $$$$\mathrm{x}=\mathrm{2y}^{\mathrm{2}} \:\mathrm{closest}\:\mathrm{to}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left(\mathrm{10},\mathrm{0}\right) \\ $$

Question Number 121257    Answers: 2   Comments: 4

If today is June 17,2009 and George was born on November 25, 1967. How old is George?

$$\mathrm{If}\:\mathrm{today}\:\mathrm{is}\:\mathrm{June}\:\mathrm{17},\mathrm{2009}\:\mathrm{and}\:\mathrm{George} \\ $$$$\mathrm{was}\:\mathrm{born}\:\mathrm{on}\:\mathrm{November}\:\mathrm{25},\:\mathrm{1967}.\: \\ $$$$\mathrm{How}\:\mathrm{old}\:\mathrm{is}\:\mathrm{George}? \\ $$

Question Number 121256    Answers: 2   Comments: 0

Prove 2sin^2 3θ−2sin^2 θ=cos2θ−cos6θ. By substitusing θ=(π/(10)) in the above identity, prove that sin((3π)/(10))−sin(π/(10))=(1/2)

$$\mathrm{Prove}\:\mathrm{2sin}^{\mathrm{2}} \mathrm{3}\theta−\mathrm{2sin}^{\mathrm{2}} \theta=\mathrm{cos2}\theta−\mathrm{cos6}\theta. \\ $$$$\mathrm{By}\:\mathrm{substitusing}\:\theta=\frac{\pi}{\mathrm{10}}\:\mathrm{in}\:\mathrm{the}\:\mathrm{above}\:\mathrm{identity}, \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{10}}−\mathrm{sin}\frac{\pi}{\mathrm{10}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 121246    Answers: 2   Comments: 0

Σ_(k=1) ^(49) (1/( (√(k+(√(k^2 −1)))))) ?

$$\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{49}} {\sum}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{k}+\sqrt{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}}}\:? \\ $$

Question Number 121244    Answers: 0   Comments: 2

Question Number 121235    Answers: 2   Comments: 0

Find the sum of n terms of the series S_n =1+22+333+4444+……

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$${S}_{{n}} =\mathrm{1}+\mathrm{22}+\mathrm{333}+\mathrm{4444}+\ldots\ldots \\ $$

Question Number 121229    Answers: 1   Comments: 0

Question Number 121227    Answers: 1   Comments: 0

(d^2 y/dx^2 ) = e^(−2x)

$$\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:=\:\mathrm{e}^{−\mathrm{2x}} \: \\ $$

Question Number 121225    Answers: 2   Comments: 0

∫_0 ^1 x^5 (√((1+x^2 )/(1−x^2 ))) dx ?

$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\mathrm{x}^{\mathrm{5}} \:\sqrt{\frac{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:? \\ $$

Question Number 121224    Answers: 1   Comments: 0

∫ cos^2 x tan^3 x dx

$$\:\:\:\:\int\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{dx}\: \\ $$

Question Number 121222    Answers: 1   Comments: 0

lim_(x→−∞) (((√(1+x^2 ))−x+1)/(x+1)) ?

$$\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{x}+\mathrm{1}}{\mathrm{x}+\mathrm{1}}\:? \\ $$

Question Number 121237    Answers: 2   Comments: 0

lim_(x→0) (((1+mx)^n −(1+nx)^m )/x^2 ) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{mx}\right)^{\mathrm{n}} −\left(\mathrm{1}+\mathrm{nx}\right)^{\mathrm{m}} }{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 121219    Answers: 1   Comments: 1

Given that a,b and c are three consecutive numbers, where a>b>c, such that its product is the same as its sum, that is abc=a+b+c, how many such (a,b,c)?

$$\mathrm{Given}\:\mathrm{that}\:{a},{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{three}\:\mathrm{consecutive} \\ $$$$\mathrm{numbers},\:\mathrm{where}\:{a}>{b}>{c},\:\mathrm{such}\:\mathrm{that}\:\mathrm{its}\:\mathrm{product} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:\mathrm{its}\:\mathrm{sum},\:\mathrm{that}\:\mathrm{is}\:{abc}={a}+{b}+{c}, \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{such}\:\left({a},{b},{c}\right)? \\ $$

Question Number 121217    Answers: 0   Comments: 0

Question Number 121215    Answers: 0   Comments: 0

Question Number 121218    Answers: 1   Comments: 0

If x=(√(1+(√2))), find the value of x^4 +(1/x^4 ).

$$\mathrm{If}\:{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{2}}},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }. \\ $$

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