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Question Number 182295    Answers: 1   Comments: 0

Question Number 182292    Answers: 3   Comments: 0

Question Number 182291    Answers: 0   Comments: 0

I_2 =∫_0 ^∞ (((tan^(−1) x)/x))^2 dx=?? I_3 =∫_0 ^∞ (((tan^(−1) x)/x))^3 dx=??? I_4 =∫_0 ^∞ (((tan^(−1) x)/x))^4 dx=????

$${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{2}} {dx}=?? \\ $$$${I}_{\mathrm{3}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{3}} {dx}=??? \\ $$$${I}_{\mathrm{4}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{4}} {dx}=???? \\ $$

Question Number 182279    Answers: 1   Comments: 0

∫_0 ^∞ ((x^(10) (1+x^5 ))/((1+x)^(27) ))dx = ?

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{10}} \left(\mathrm{1}+{x}^{\mathrm{5}} \right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{27}} }{dx}\:=\:? \\ $$

Question Number 182270    Answers: 0   Comments: 0

Question Number 182256    Answers: 1   Comments: 0

Question Number 182253    Answers: 0   Comments: 3

Question Number 182252    Answers: 0   Comments: 0

Question Number 182272    Answers: 2   Comments: 1

1≤a≤37 1≤b≤37 1+7a+8b +19ab = 0 mod(37) a and b natural nambers (a_1 ;b_1 ) (a_2 ;b_2 )......(a_n ;b_n ) n=?

$$\:\:\:\:\mathrm{1}\leqslant\boldsymbol{\mathrm{a}}\leqslant\mathrm{37} \\ $$$$\:\:\:\:\mathrm{1}\leqslant\boldsymbol{\mathrm{b}}\leqslant\mathrm{37} \\ $$$$\:\:\:\mathrm{1}+\mathrm{7a}+\mathrm{8}\boldsymbol{\mathrm{b}}\:+\mathrm{19}\boldsymbol{\mathrm{ab}}\:\:=\:\mathrm{0}\:\boldsymbol{\mathrm{mod}}\left(\mathrm{37}\right)\: \\ $$$$\:\:\boldsymbol{\mathrm{a}}\:\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{b}}\:\:\boldsymbol{\mathrm{natural}}\:\:\boldsymbol{\mathrm{nambers}} \\ $$$$\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}_{\mathrm{1}} ;\boldsymbol{\mathrm{b}}_{\mathrm{1}} \right)\:\left(\boldsymbol{\mathrm{a}}_{\mathrm{2}} ;\boldsymbol{\mathrm{b}}_{\mathrm{2}} \right)......\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \right) \\ $$$$\:\:\:\boldsymbol{\mathrm{n}}=? \\ $$$$\:\:\:\: \\ $$

Question Number 182271    Answers: 2   Comments: 0

Question Number 182247    Answers: 2   Comments: 0

Find: (√(9 + 4 (√5))) − (√(9 − 4 (√5))) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{9}\:+\:\mathrm{4}\:\sqrt{\mathrm{5}}}\:−\:\sqrt{\mathrm{9}\:−\:\mathrm{4}\:\sqrt{\mathrm{5}}}\:=\:? \\ $$

Question Number 182242    Answers: 1   Comments: 0

∫^2 _0 ∫^3 _0 ∫^4 _0 e^(x+y+z) dx dy dz=?

$$\underset{\mathrm{0}} {\int}^{\mathrm{2}} \underset{\mathrm{0}} {\int}^{\mathrm{3}} \underset{\mathrm{0}} {\int}^{\mathrm{4}} {e}^{{x}+{y}+{z}} \:{dx}\:{dy}\:{dz}=? \\ $$

Question Number 182241    Answers: 0   Comments: 0

It is given a family of open interval set (U_r )_(r∈Q) of R that satifies condition ∀r∈Q, r∈U_(r ) . Prove that there exists a family set (U_r )_(r∈Q) which not cover R or ∀ε>0, λ(∪_(r∈Q) U_r )≤ ε .

$$\:\mathrm{It}\:\mathrm{is}\:\mathrm{given}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\:\mathrm{open}\:\mathrm{interval}\:\mathrm{set}\:\left({U}_{{r}} \right)_{{r}\in\mathbb{Q}} \:\mathrm{of}\:\mathbb{R} \\ $$$$\mathrm{that}\:\mathrm{satifies}\:\mathrm{condition}\:\forall{r}\in\mathbb{Q},\:{r}\in{U}_{{r}\:} . \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{family}\:\mathrm{set}\:\left({U}_{{r}} \right)_{{r}\in\mathbb{Q}} \mathrm{which}\:\mathrm{not}\:\mathrm{cover}\:\mathbb{R}\: \\ $$$$\mathrm{or}\:\forall\varepsilon>\mathrm{0},\:\:\lambda\left(\underset{{r}\in\mathbb{Q}} {\cup}\:{U}_{{r}} \:\right)\leqslant\:\varepsilon\:. \\ $$

Question Number 182238    Answers: 1   Comments: 0

Question Number 182280    Answers: 1   Comments: 2

Question Number 182203    Answers: 0   Comments: 0

Let A={1^(p^2 −p) , 2^(p^2 −p) ,..., (p−1)^(p^2 −p) , p^2 −p+1} where p is any prime number Prove that for any value of p, however we split this set into two disjunctive sets, the arithmetic means of all elements of both sets cannot be equal to each other.

$${Let}\:{A}=\left\{\mathrm{1}^{{p}^{\mathrm{2}} −{p}} ,\:\mathrm{2}^{{p}^{\mathrm{2}} −{p}} ,...,\:\left({p}−\mathrm{1}\right)^{{p}^{\mathrm{2}} −{p}} ,\:{p}^{\mathrm{2}} −{p}+\mathrm{1}\right\} \\ $$$${where}\:{p}\:{is}\:{any}\:{prime}\:{number} \\ $$$${Prove}\:{that}\:{for}\:{any}\:{value}\:{of}\:{p}, \\ $$$${however}\:{we}\:{split}\:{this}\:{set}\:{into}\:{two} \\ $$$${disjunctive}\:{sets},\:{the}\:{arithmetic} \\ $$$${means}\:{of}\:{all}\:{elements}\:{of}\:{both}\:{sets} \\ $$$${cannot}\:{be}\:{equal}\:{to}\:{each}\:{other}. \\ $$

Question Number 182200    Answers: 2   Comments: 0

1. lim_(a→−x) ((sin(x^2 − a^2 ))/(x^3 + a^3 )) = ? 2. cot 80° (tan 10° + 2 tg 70°) = ?

$$\mathrm{1}.\:\:\:\underset{\boldsymbol{\mathrm{a}}\rightarrow−\boldsymbol{\mathrm{x}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$$$ \\ $$$$\mathrm{2}.\:\:\:\mathrm{cot}\:\mathrm{80}°\:\left(\mathrm{tan}\:\mathrm{10}°\:+\:\mathrm{2}\:\mathrm{tg}\:\mathrm{70}°\right)\:=\:? \\ $$

Question Number 182199    Answers: 2   Comments: 0

Let S={1, 2, 3, 4, 5, 6, 7} If we multiply atleast 2 numbers from this set with each other, what are the chances of the product to turn out to be divisible by 3?

$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

Question Number 182192    Answers: 1   Comments: 1

Question Number 182188    Answers: 2   Comments: 0

((((√5)+2))^(1/3) +(((√5)−2))^(1/3) )^(2014) =?

$$\left(\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}+\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}}\right)^{\mathrm{2014}} =? \\ $$

Question Number 182183    Answers: 1   Comments: 0

∫_0 ^( 1) e^a a^n da=? n≥1 n∈N

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \boldsymbol{{e}}^{\boldsymbol{{a}}} \boldsymbol{{a}}^{\boldsymbol{{n}}} \boldsymbol{{da}}=?\:\:\:\:\:\:\:\:\boldsymbol{{n}}\geqslant\mathrm{1}\:\:\:\:\boldsymbol{{n}}\in\boldsymbol{{N}} \\ $$

Question Number 182178    Answers: 1   Comments: 2

The Circle Has A Radius 5cm And the angle between sector from the chord is 73.7397952916880° and their right triangle is AB=4 cm AC=3 cm Find the area of arc triangle EDB with E^⌢ D^⌢ is arc

$${The}\:{Circle}\:{Has}\:{A}\:{Radius}\:\mathrm{5}{cm} \\ $$$${And}\:{the}\:{angle}\:{between} \\ $$$$\:{sector}\:{from}\:{the}\:{chord}\:{is} \\ $$$$\mathrm{73}.\mathrm{7397952916880}° \\ $$$${and}\:{their}\:{right}\:{triangle}\:{is} \\ $$$${AB}=\mathrm{4}\:{cm} \\ $$$${AC}=\mathrm{3}\:{cm} \\ $$$${Find}\:{the}\:{area}\:{of}\:{arc}\:{triangle} \\ $$$${EDB} \\ $$$${with}\:\overset{\frown} {{E}}\overset{\frown} {{D}}\:{is}\:{arc} \\ $$$$ \\ $$

Question Number 182176    Answers: 1   Comments: 0

Question Number 182170    Answers: 1   Comments: 0

Question Number 182165    Answers: 0   Comments: 1

Question Number 182155    Answers: 3   Comments: 1

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