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Question Number 201463 Answers: 1 Comments: 0

a = constant number: if ∫x ∙ f(x) dx = x^3 - x^2 + 4x - (a/5) find f(2) = ?

$$\mathrm{a}\:=\:\mathrm{constant}\:\mathrm{number}: \\ $$$$\mathrm{if}\:\:\:\int\mathrm{x}\:\centerdot\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:-\:\frac{\mathrm{a}}{\mathrm{5}} \\ $$$$\mathrm{find}\:\:\:\mathrm{f}\left(\mathrm{2}\right)\:=\:? \\ $$

Question Number 201462 Answers: 1 Comments: 0

Find: ∫_0 ^( 𝛑) (√(1 - 4 sin^2 (x/2) cos^2 (x/2))) dx = ?

$$\mathrm{Find}: \\ $$$$\int_{\mathrm{0}} ^{\:\boldsymbol{\pi}} \:\sqrt{\mathrm{1}\:-\:\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{cos}^{\mathrm{2}} \:\frac{\mathrm{x}}{\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 201456 Answers: 1 Comments: 0

Question Number 201460 Answers: 1 Comments: 0

Find the smallest positive period of the function: y = ∣ tan 2x ∣ + ∣ cot 2x ∣

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{function}: \\ $$$$\mathrm{y}\:=\:\mid\:\mathrm{tan}\:\mathrm{2x}\:\mid\:\:+\:\:\mid\:\mathrm{cot}\:\mathrm{2x}\:\mid \\ $$

Question Number 201332 Answers: 1 Comments: 0

calcul : 1. lim_(n→+∞ ) ((sin(n^2 )−cos(n^3 ))/n) 2. lim_(n→+∞) ^n (√(3−sin(n^2 ))) 3. lim_(n→+∞) (n/(n+1)) e^(i((nπ)/3))

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:{calcul}\:: \\ $$$$ \\ $$$$\:\:\:\:\mathrm{1}.\:\:\:\:{lim}_{{n}\rightarrow+\infty\:} \frac{{sin}\left({n}^{\mathrm{2}} \right)−{cos}\left({n}^{\mathrm{3}} \right)}{{n}}\: \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{2}.\:\:\:\:\:{lim}_{{n}\rightarrow+\infty} \:^{{n}} \sqrt{\mathrm{3}−{sin}\left({n}^{\mathrm{2}} \right)} \\ $$$$ \\ $$$$\:\:\:\:\:\mathrm{3}.\:\:\:\:\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{n}}{{n}+\mathrm{1}}\:{e}^{{i}\frac{{n}\pi}{\mathrm{3}}} \: \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 201329 Answers: 1 Comments: 0

Question Number 201325 Answers: 1 Comments: 1

Question Number 201323 Answers: 0 Comments: 0

Question Number 201322 Answers: 1 Comments: 0

Question Number 201491 Answers: 6 Comments: 1

1. x^2 −1+((x^4 −x^2 ))^(1/3) =10x 2. (√(x−(1/x)))+(√(1−(1/x)))=x 3. (√(2x−(8/x)))+2(√(1−(2/x)))≥x 4. (√(x^2 +x))+(√(x+2))≥(√(3(x^2 −2x+2))) 5. ((√(x+5))−(√(x−3)))(1+(√(x^2 +2x−15)))≥8 6. x^2 +3x+1=(x+1)(√(x^2 +1)) 7. 2x^2 +3x+7=(x+5)(√(2x^2 +1))

$$\mathrm{1}.\:{x}^{\mathrm{2}} −\mathrm{1}+\sqrt[{\mathrm{3}}]{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} }=\mathrm{10}{x} \\ $$$$\mathrm{2}.\:\sqrt{{x}−\frac{\mathrm{1}}{{x}}}+\sqrt{\mathrm{1}−\frac{\mathrm{1}}{{x}}}={x} \\ $$$$\mathrm{3}.\:\sqrt{\mathrm{2}{x}−\frac{\mathrm{8}}{{x}}}+\mathrm{2}\sqrt{\mathrm{1}−\frac{\mathrm{2}}{{x}}}\geqslant{x} \\ $$$$\mathrm{4}.\:\sqrt{{x}^{\mathrm{2}} +{x}}+\sqrt{{x}+\mathrm{2}}\geqslant\sqrt{\mathrm{3}\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)} \\ $$$$\mathrm{5}.\:\left(\sqrt{{x}+\mathrm{5}}−\sqrt{{x}−\mathrm{3}}\right)\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{15}}\right)\geqslant\mathrm{8} \\ $$$$\mathrm{6}.\:{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}=\left({x}+\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\mathrm{7}.\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{7}=\left({x}+\mathrm{5}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 201308 Answers: 1 Comments: 2