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Question Number 86024 Answers: 1 Comments: 1

last three digits of 951413^(314159) =?

$$\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of} \\ $$$$\mathrm{951413}^{\mathrm{314159}} =? \\ $$

Question Number 86021 Answers: 0 Comments: 3

E is a vectorial plan in R with a base B=(i^→ ,j^→ ). f is an endomorphism of E defined ∀ u^→ =xi^→ +yj^→ by f(u^→ )=(−7x−12y)i^→ +(4x+7y)j^→ . 1) Determinate f(i^→ ) and f(j^→ ) then write the matrice of f in (i^→ ,j^→ )base.

Question Number 86018 Answers: 2 Comments: 0

Find the three last digits of 5^(9999) .

$${Find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\mathrm{5}^{\mathrm{9999}} . \\ $$

Question Number 86016 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((x^2 −3)/((x^2 +1)^7 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{3}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{7}} }{dx} \\ $$

Question Number 86015 Answers: 0 Comments: 0

calculate ∫_0 ^(+∞) (dx/((x^2 −x+2)^4 ))

$${calculate}\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 86013 Answers: 0 Comments: 1

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

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

Question Number 86009 Answers: 1 Comments: 0

solve in R :[(x/2)]+[((2x)/3)]−x=0

$${solve}\:{in}\:{R}\::\left[\frac{{x}}{\mathrm{2}}\right]+\left[\frac{\mathrm{2}{x}}{\mathrm{3}}\right]−{x}=\mathrm{0} \\ $$

Question Number 86008 Answers: 0 Comments: 3

Question Number 86062 Answers: 2 Comments: 1

∫((√(x^2 −25))/x)dx

$$\int\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{25}}}{{x}}{dx} \\ $$

Question Number 86003 Answers: 1 Comments: 1

y ′′ + y′ = sin x cos 2x

$$\mathrm{y}\:''\:+\:\mathrm{y}'\:=\:\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x} \\ $$

Question Number 86000 Answers: 1 Comments: 0

solve the equation x^(1/3) =4

$${solve}\:{the}\:{equation}\:\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} =\mathrm{4} \\ $$

Question Number 85999 Answers: 0 Comments: 5

∫_0 ^∞ ((sinx^2 )/(1+x^4 ))dx=0.4009 prove that

$$\int_{\mathrm{0}} ^{\infty} \frac{{sinx}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{4}} }{dx}=\mathrm{0}.\mathrm{4009} \\ $$$${prove}\:{that} \\ $$

Question Number 85985 Answers: 0 Comments: 0

Consider the functionf defined by parf(x) = −x + ((ln x)/x) in the interval : ]0,+∞[. (C_f ) is its representative curve in an orthonormal reference system (O,i^→ ,j^→ ). Calculate lim_(x→0^+ ) f(x), lim_(x→+∞) f(x).

$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{function}{f}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{par}{f}\left({x}\right)\:=\:−{x}\:+\:\frac{\mathrm{ln}\:{x}}{{x}}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval} \\ $$$$\left.:\:\right]\mathrm{0},+\infty\left[.\:\:\left({C}_{{f}} \right)\:\mathrm{is}\:\mathrm{its}\:\mathrm{representative}\:\mathrm{curve}\:\mathrm{in}\:\mathrm{an}\:\mathrm{orthonormal}\right. \\ $$$$\mathrm{reference}\:\mathrm{system}\:\left(\mathrm{O},\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right). \\ $$$$\:\mathrm{Calculate}\:\:\underset{{x}\rightarrow\mathrm{0}^{+} \:} {\mathrm{lim}}\:{f}\left({x}\right),\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}\right). \\ $$

Question Number 86063 Answers: 1 Comments: 0

Question Number 85982 Answers: 0 Comments: 2

A primitive of the function defned by f(x) = x −1 + (1/(x+1)) is A. F(x) = (x^2 /2) −x + ln(x + 1) B. F(x) = (x^2 /2) + ln(x−1) C. F(x) = (x^2 /2)−x + ln(1−x) D. F(x) = −x + ln(x−1)

$$\mathrm{A}\:\mathrm{primitive}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{defned}\:\mathrm{by}\:\mathrm{f}\left({x}\right)\:=\:{x}\:−\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:\mathrm{is}\: \\ $$$$\mathrm{A}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:−{x}\:+\:\mathrm{ln}\left({x}\:+\:\mathrm{1}\right)\:\:\:\:\mathrm{B}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$\mathrm{C}.\:\mathrm{F}\left({x}\right)\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}−{x}\:+\:\mathrm{ln}\left(\mathrm{1}−{x}\right)\:\:\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{F}\left({x}\right)\:=\:−{x}\:+\:\mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$

Question Number 85961 Answers: 0 Comments: 4