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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

Question Number 162673 Answers: 1 Comments: 0

Question Number 162672 Answers: 2 Comments: 0

Calculate lim_(x→+∞) (((x^3 +3x^2 ))^(1/3) −(√(x^2 −2x))) lim_(x→7) (((√(x+2))−((x+20))^(1/3) )/( ((x+9))^(1/4) −2))

$${Calculate} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}}\right) \\ $$$$\underset{{x}\rightarrow\mathrm{7}} {\mathrm{lim}}\frac{\sqrt{{x}+\mathrm{2}}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{20}}}{\:\sqrt[{\mathrm{4}}]{{x}+\mathrm{9}}−\mathrm{2}} \\ $$

Question Number 162651 Answers: 1 Comments: 0

Question Number 162649 Answers: 3 Comments: 0

sin^(10) (x)+cos^(10) (x)=((11)/(36)) sin^(12) (x)+cos^(12) (x)=?

$$\:\mathrm{sin}\:^{\mathrm{10}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{10}} \left({x}\right)=\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\:\mathrm{sin}\:^{\mathrm{12}} \left({x}\right)+\mathrm{cos}\:^{\mathrm{12}} \left({x}\right)=? \\ $$

Question Number 162643 Answers: 3 Comments: 0

lim_(x→∞) x^(4/3) (((x^2 +1))^(1/3) + ((3−x^2 ))^(1/3) ) =?

$$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{4}/\mathrm{3}} \:\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{3}−{x}^{\mathrm{2}} }\:\right)\:=? \\ $$

Question Number 162622 Answers: 3 Comments: 0

Solve for real numbers: x^(12) - 15x^3 + 14 = 0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{12}} \:-\:\mathrm{15x}^{\mathrm{3}} \:+\:\mathrm{14}\:=\:\mathrm{0} \\ $$

Question Number 162618 Answers: 2 Comments: 0

Calculate lim_(x→∞) (5^x +8^x )^(1/(3x))

$${Calculate} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{5}^{{x}} +\mathrm{8}^{{x}} \right)^{\frac{\mathrm{1}}{\mathrm{3}{x}}} \\ $$

Question Number 162604 Answers: 1 Comments: 0

I=∫_0 ^(π/4) xtg(x)dx=?

$${I}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \boldsymbol{{xtg}}\left(\boldsymbol{{x}}\right)\boldsymbol{{dx}}=? \\ $$

Question Number 162598 Answers: 1 Comments: 0

Question Number 162589 Answers: 1 Comments: 0

Question Number 162585 Answers: 1 Comments: 0

lim_(n→∞) (2n∫_0 ^1 (x^n /(1+x^2 ))dx)^n =?

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

Question Number 162584 Answers: 1 Comments: 0

prove that ppcm(a,b)×pgcd(a,b)=∣ab∣

$${prove}\:{that} \\ $$$${ppcm}\left({a},{b}\right)×{pgcd}\left({a},{b}\right)=\mid{ab}\mid \\ $$

Question Number 162575 Answers: 2 Comments: 0

∫_0 ^π (x^2 /(1+sinx))dx

$$\int_{\mathrm{0}} ^{\pi} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{sin}{x}}{dx} \\ $$

Question Number 162561 Answers: 2 Comments: 0

Question Number 162560 Answers: 0 Comments: 1

Question Number 162552 Answers: 1 Comments: 1

𝛂_1 <𝛂_2 <𝛂_3 <…<𝛂_k ((2^(289) +1)/(2^(17) +1))=2^𝛂_1 +2^𝛂_2 +…+2^𝛂_k k=? 𝛂_1 , 𝛂_2 ,𝛂_3 ....𝛂_k positive increasing integers

Question Number 162539 Answers: 2 Comments: 0

Calculate lim_(h→0) ((f(3−h)−f(3))/(2h)), with f′(3)=2

$${Calculate}\: \\ $$$$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left(\mathrm{3}−{h}\right)−{f}\left(\mathrm{3}\right)}{\mathrm{2}{h}},\:{with}\:{f}'\left(\mathrm{3}\right)=\mathrm{2} \\ $$

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