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Question Number 162794 Answers: 0 Comments: 0

Question Number 162792 Answers: 1 Comments: 0

Find: 𝛀 = ∫_( 0) ^( ∞) ((arctan(x))/(x∙(x^2 - x + 1))) dx

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{arctan}\left(\mathrm{x}\right)}{\mathrm{x}\centerdot\left(\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{x}\:+\:\mathrm{1}\right)}\:\mathrm{dx} \\ $$

Question Number 162791 Answers: 3 Comments: 0

Question Number 162790 Answers: 1 Comments: 0

Calculate lim_(n→∞) (1+2^n +3^n )^(1/n)

$${Calculate}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{2}^{{n}} +\mathrm{3}^{{n}} \right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 162788 Answers: 1 Comments: 0

let x;y;z > 0 such that x^4 +y^4 +z^4 = x^2 +y^2 +z^2 find the minimum of the expression: P = (x^2 /y) + (y^2 /z) + (z^2 /x)

$$\mathrm{let}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\:>\:\mathrm{0} \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\mathrm{x}^{\mathrm{4}} +\mathrm{y}^{\mathrm{4}} +\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{P}\:=\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{y}}\:+\:\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{z}}\:+\:\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{x}} \\ $$

Question Number 162787 Answers: 1 Comments: 0

happy new year {a;b;c}∈Z−{0} p(x)=ax^2 +bx+c p(a)=0 p(b)=0 p(1)=?

$$\boldsymbol{\mathrm{happy}}\:\boldsymbol{\mathrm{new}}\:\boldsymbol{\mathrm{year}} \\ $$$$\left\{\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\right\}\in\mathbb{Z}−\left\{\mathrm{0}\right\} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{ax}}^{\mathrm{2}} +\boldsymbol{{bx}}+\boldsymbol{{c}}\:\:\:\: \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{a}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{b}}\right)=\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\mathrm{1}\right)=? \\ $$

Question Number 162783 Answers: 0 Comments: 0

Question Number 162782 Answers: 0 Comments: 0

Question Number 162776 Answers: 3 Comments: 0

((sin x)/(1−cos x)) = (1/2) x=?

$$\:\:\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{cos}\:{x}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\: \\ $$$$\:{x}=? \\ $$

Question Number 162775 Answers: 2 Comments: 0

lim_(x→0) ((a sin 3x − b sin 2x )/x^3 ) = (1/2) Find a and b .

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}\:\mathrm{sin}\:\mathrm{3}{x}\:−\:{b}\:\mathrm{sin}\:\mathrm{2}{x}\:}{{x}^{\mathrm{3}} }\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\:{Find}\:{a}\:{and}\:{b}\:. \\ $$

Question Number 162785 Answers: 1 Comments: 0

Question Number 162747 Answers: 1 Comments: 0

Question Number 162744 Answers: 0 Comments: 0

Question Number 162734 Answers: 1 Comments: 0

Happy New Year [(10+9)×8×(7+6)+(5+4)×(3+2)+1]

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Happy}\:{New}\:{Year} \\ $$$$\left[\left(\mathrm{10}+\mathrm{9}\right)×\mathrm{8}×\left(\mathrm{7}+\mathrm{6}\right)+\left(\mathrm{5}+\mathrm{4}\right)×\left(\mathrm{3}+\mathrm{2}\right)+\mathrm{1}\right] \\ $$

Question Number 163110 Answers: 1 Comments: 0

Question Number 162728 Answers: 2 Comments: 2

Question Number 162726 Answers: 1 Comments: 0

1) Calculate lim_(x→0) ((tgx^m )/((sin x)^n )), (m, n∈ N) 2) f′(a) existe, calculate lim_(x→+∞) x[f(a+(a/x))−f(a−(β/x))], (α, β ∈ R)

$$\left.\mathrm{1}\right)\:{Calculate} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{tgx}^{{m}} }{\left(\mathrm{sin}\:{x}\right)^{{n}} },\:\:\left({m},\:{n}\in\: {N}\right) \\ $$$$\left.\mathrm{2}\right)\:{f}'\left({a}\right)\:{e}\mathrm{xiste},\:{calculate} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{x}\left[{f}\left({a}+\frac{{a}}{{x}}\right)−{f}\left({a}−\frac{\beta}{{x}}\right)\right],\: \\ $$$$\left(\alpha,\:\beta\:\in\: {R}\right) \\ $$

Question Number 162718 Answers: 0 Comments: 0

lim_(n→∞) ((∫_ε ^1 (1−x^2 )^n dx)/(∫_0 ^1 (1−x^2 )^n dx))=? (0<ε<1)

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\int_{\epsilon} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} \mathrm{dx}}=?\:\:\:\:\:\:\:\left(\mathrm{0}<\epsilon<\mathrm{1}\right) \\ $$

Question Number 162702 Answers: 0 Comments: 0

∫e^(−4x) tg(x)ln∣cos(x)∣dx=?

$$\int\boldsymbol{{e}}^{−\mathrm{4}\boldsymbol{{x}}} \boldsymbol{{tg}}\left(\boldsymbol{{x}}\right)\boldsymbol{{ln}}\mid\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\mid\boldsymbol{{dx}}=? \\ $$

Question Number 162701 Answers: 1 Comments: 0

Question Number 164806 Answers: 1 Comments: 7

Question Number 162721 Answers: 3 Comments: 0

calculate f (x )= (( 1)/(4(1+cos ((x/2))) )) +(1/(9(1−cos ((x/2))))) ( x ≠ 2k π , k ∈ Z) f_( min) = ? Adapted From Instagram

$$ \\ $$$$\:\:\:\:\:\:\:{calculate}\: \\ $$$$\:\:\:\:\:\:{f}\:\left({x}\:\right)=\:\frac{\:\mathrm{1}}{\mathrm{4}\left(\mathrm{1}+{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right)\:}\:+\frac{\mathrm{1}}{\mathrm{9}\left(\mathrm{1}−{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)\right)}\:\:\left(\:{x}\:\neq\:\mathrm{2}{k}\:\pi\:,\:{k}\:\in\:\mathbb{Z}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{f}_{\:{min}} =\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathscr{A}{dapted}\:\mathscr{F}{rom}\:\mathscr{I}{nstagram}\: \\ $$$$ \\ $$

Question Number 163178 Answers: 1 Comments: 0

Question Number 162715 Answers: 2 Comments: 0

∣∣x−1∣−5∣ ≥ 2 has solution set is a ≤x≤b or x≤ c ∪ x≥d . Find ((a+d)/(b+c)) .

$$\:\:\:\mid\mid{x}−\mathrm{1}\mid−\mathrm{5}\mid\:\geqslant\:\mathrm{2}\:\:{has}\:{solution}\:{set} \\ $$$$\:{is}\:{a}\:\leqslant{x}\leqslant{b}\:{or}\:{x}\leqslant\:{c}\:\cup\:{x}\geqslant{d}\:. \\ $$$$\:{Find}\:\frac{{a}+{d}}{{b}+{c}}\:. \\ $$

Question Number 162675 Answers: 1 Comments: 0

y = (√x) Find (dy/dx) by first principle.

$${y}\:=\:\sqrt{{x}} \\ $$$${Find}\:\:\:\frac{{dy}}{{dx}}\:\:{by}\:{first}\:{principle}. \\ $$

Question Number 162674 Answers: 2 Comments: 0

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