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Question Number 71838    Answers: 1   Comments: 3

solve the system of linear congruences x ≡ 2 (mod 3) x ≡ 4(mod 5) x ≡ 7 (mod 9) x≡ 11( mod 13) using the Brute force method

$${solve}\:{the}\:{system}\:{of}\:{linear}\:{congruences}\: \\ $$$$\:{x}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{3}\right) \\ $$$${x}\:\equiv\:\mathrm{4}\left({mod}\:\mathrm{5}\right) \\ $$$${x}\:\equiv\:\mathrm{7}\:\left({mod}\:\mathrm{9}\right) \\ $$$${x}\equiv\:\mathrm{11}\left(\:{mod}\:\mathrm{13}\right) \\ $$$${using}\:{the}\:{Brute}\:{force}\:{method} \\ $$

Question Number 71831    Answers: 1   Comments: 2

Question Number 71824    Answers: 2   Comments: 1

solve x^x^x^(2019) =2019

$${solve}\: \\ $$$${x}^{{x}^{{x}^{\mathrm{2019}} } } =\mathrm{2019} \\ $$

Question Number 71819    Answers: 1   Comments: 3

There are 3 tangent circumferences inscribed in an isosceles right triangle Two of these circumferences have radius R and are tangent to the hypotenuse and to the two cathetus. The smaller circumference has radius r and is tangent to the two cathetus. How can I find the radius of the smaller circumference as a function of R? (I want a tip on how to solve the problem).

$${There}\:{are}\:\mathrm{3}\:{tangent}\:{circumferences} \\ $$$${inscribed}\:{in}\:{an}\:{isosceles}\:{right}\:{triangle} \\ $$$${Two}\:{of}\:{these}\:{circumferences}\:{have} \\ $$$${radius}\:\boldsymbol{{R}}\:{and}\:{are}\:{tangent}\:{to}\:{the}\: \\ $$$${hypotenuse}\:{and}\:{to}\:{the}\:{two}\:{cathetus}. \\ $$$${The}\:{smaller}\:{circumference}\:{has}\: \\ $$$${radius}\:\boldsymbol{{r}}\:{and}\:{is}\:{tangent}\:{to}\:{the}\:{two} \\ $$$${cathetus}.\:{How}\:{can}\:{I}\:{find}\:{the}\:{radius} \\ $$$${of}\:{the}\:{smaller}\:{circumference}\:{as}\:{a} \\ $$$${function}\:{of}\:\boldsymbol{{R}}? \\ $$$$\left({I}\:{want}\:{a}\:{tip}\:{on}\:{how}\:{to}\:{solve}\:{the}\:\right. \\ $$$$\left.{problem}\right). \\ $$

Question Number 71816    Answers: 1   Comments: 0

suppose that f is continuous and differentiable in (a,b) if f′(x) =0 ,∀ x∈(a,b) then show that f is constant on [a,b].

$${suppose}\:{that}\:{f}\:{is}\:{continuous}\:{and}\:{differentiable}\:{in}\:\left({a},{b}\right)\:{if}\:{f}'\left({x}\right)\:=\mathrm{0}\:,\forall\:{x}\in\left({a},{b}\right)\:{then}\:{show}\:{that}\:{f}\:{is}\:{constant}\:{on}\:\left[{a},{b}\right]. \\ $$

Question Number 71814    Answers: 1   Comments: 2

∫(1/(1+cot x))dx

$$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:{x}}{dx} \\ $$

Question Number 71813    Answers: 0   Comments: 0

1)calculate F(a)=∫_0 ^(π/4) arctan(1+a cosx)dx 2)find the valeur of ∫_0 ^(π/4) arctan(1+(√2)cosx)dx

$$\left.\mathrm{1}\right){calculate}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {arctan}\left(\mathrm{1}+{a}\:{cosx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{valeur}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{arctan}\left(\mathrm{1}+\sqrt{\mathrm{2}}{cosx}\right){dx} \\ $$

Question Number 71810    Answers: 0   Comments: 0

Question Number 71809    Answers: 1   Comments: 0

Question Number 71806    Answers: 1   Comments: 0

Question Number 71802    Answers: 1   Comments: 1

find ∫ ((x^2 −1)/((x+3)^2 (x^3 −5x+4)))dx

$${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{5}{x}+\mathrm{4}\right)}{dx} \\ $$

Question Number 71801    Answers: 0   Comments: 0

find I_n =∫_0 ^1 x^n (√(1+x^2 ))dx with n integr natural

$${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 71799    Answers: 2   Comments: 0

Question Number 71777    Answers: 0   Comments: 1

lim_(n→∞) (((n! + 3^n )/(n^n + 3^n ))) = ?

$$\:\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{lim}}}\:\left(\frac{\boldsymbol{{n}}!\:+\:\mathrm{3}^{\boldsymbol{{n}}} }{\boldsymbol{{n}}^{\boldsymbol{{n}}} \:+\:\mathrm{3}^{\boldsymbol{{n}}} }\right)\:=\:? \\ $$

Question Number 71776    Answers: 1   Comments: 0

Question Number 71769    Answers: 0   Comments: 3

show that if f is a differentiable function at the point x=a, then f is continuous at x=a.

$${show}\:{that}\:{if}\:{f}\:{is}\:{a}\:{differentiable}\:{function}\:{at}\:{the}\:{point}\:{x}={a},\:{then}\:{f}\:{is}\:{continuous}\:{at}\:{x}={a}. \\ $$

Question Number 71767    Answers: 0   Comments: 0

Let f be continuous on a closed and bounded subset E, then show that f is uniformly continuous.

$${Let}\:{f}\:{be}\:{continuous}\:{on}\:{a}\:{closed}\:{and}\:{bounded}\:{subset}\:{E},\:{then}\:{show}\:{that}\:{f}\:{is}\:{uniformly}\:{continuous}. \\ $$

Question Number 71761    Answers: 0   Comments: 5

Find at least the first four non zero term in a power series expansion about x = 0 for a general solution to z′′ − x^2 z = 0

$$\mathrm{Find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{power} \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{about}\:\:\mathrm{x}\:\:=\:\:\mathrm{0}\:\:\mathrm{for}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\mathrm{to}\:\:\:\:\mathrm{z}''\:\:−\:\:\mathrm{x}^{\mathrm{2}} \mathrm{z}\:\:\:=\:\:\mathrm{0} \\ $$

Question Number 71751    Answers: 0   Comments: 0

Question Number 71750    Answers: 0   Comments: 2

∫ cos^3 θ (1 − sin^3 θ) Using beta function

$$\int\:\mathrm{cos}^{\mathrm{3}} \theta\:\left(\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{3}} \theta\right) \\ $$$$\mathrm{Using}\:\mathrm{beta}\:\mathrm{function} \\ $$

Question Number 71740    Answers: 0   Comments: 1

Derive the expression for the pressure exerted by an ideal gas on the wall of container

$${Derive}\:{the}\:{expression} \\ $$$${for}\:{the}\:{pressure}\:{exerted} \\ $$$${by}\:{an}\:{ideal}\:{gas}\:{on}\:{the} \\ $$$${wall}\:{of}\:{container} \\ $$

Question Number 71739    Answers: 2   Comments: 0

find the asymptote of folium of Descartes x^3 +y^3 =3axy, and a is a constant >0

$${find}\:{the}\:{asymptote}\:{of}\:{folium}\:{of}\: \\ $$$${Descartes}\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{3}{axy},\:{and}\:{a}\:{is}\:{a} \\ $$$${constant}\:>\mathrm{0} \\ $$

Question Number 71729    Answers: 1   Comments: 2

find dU if U=x^2 e^(x/y)

$${find}\:{dU}\:\:\:{if}\:\:\:{U}={x}^{\mathrm{2}} {e}^{\frac{{x}}{{y}}} \\ $$$$ \\ $$

Question Number 71724    Answers: 0   Comments: 0

Question Number 71759    Answers: 0   Comments: 2

Question Number 71790    Answers: 1   Comments: 0

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