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AllQuestion and Answers: Page 521

Question Number 167393 Answers: 1 Comments: 0

Question Number 167392 Answers: 2 Comments: 0

f(x)=n! ((df(x)^n )/(d(x)^n ))=?

$${f}\left({x}\right)={n}! \\ $$$$\frac{{df}\left({x}\right)^{{n}} }{{d}\left({x}\right)^{{n}} }=? \\ $$

Question Number 167386 Answers: 0 Comments: 0

show that (A⊕B)′ = A ∩ B

$$\:\boldsymbol{{show}}\:\boldsymbol{{that}}\: \\ $$$$\:\left(\boldsymbol{{A}}\oplus\boldsymbol{{B}}\right)'\:=\:\boldsymbol{{A}}\:\cap\:\boldsymbol{{B}} \\ $$

Question Number 167380 Answers: 0 Comments: 3

show that A′ ∪ B′ ∪ C′ =(A∪B∪C)′

$$\:\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\:\boldsymbol{{A}}'\:\cup\:\boldsymbol{{B}}'\:\cup\:\boldsymbol{{C}}'\:=\left(\boldsymbol{{A}}\cup\boldsymbol{{B}}\cup\boldsymbol{{C}}\right)' \\ $$

Question Number 167374 Answers: 2 Comments: 0

Question Number 167372 Answers: 1 Comments: 0

Calculate ∫_(−2) ^2 (∣x∣+x)e^(−∣x∣) dx

$${Calculate}\: \\ $$$$\int_{−\mathrm{2}} ^{\mathrm{2}} \left(\mid{x}\mid+{x}\right){e}^{−\mid{x}\mid} {dx} \\ $$

Question Number 167366 Answers: 0 Comments: 0

Question Number 167367 Answers: 1 Comments: 1

Question Number 167360 Answers: 1 Comments: 0

∫(dx/(1+(√x)+(√(1+x))))

$$\int\frac{{dx}}{\mathrm{1}+\sqrt{{x}}+\sqrt{\mathrm{1}+{x}}} \\ $$

Question Number 167357 Answers: 1 Comments: 0

find n^(th) dervaiteve of ln(cosx) ?

$${find}\:{n}^{{th}} \:{dervaiteve}\:{of}\:{ln}\left({cosx}\right)\:? \\ $$

Question Number 167355 Answers: 0 Comments: 4

Question Number 167350 Answers: 1 Comments: 0

Question Number 167339 Answers: 2 Comments: 1

Question Number 167336 Answers: 1 Comments: 0

0< x<(π/2) f(x)= ((sin(x) ))^(1/(20)) + ((cos(x)))^(1/(20)) R_( f) =? (Range )

$$ \\ $$$$\:\:\:\:\:\:\:\:\mathrm{0}<\:{x}<\frac{\pi}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{f}\left({x}\right)=\:\sqrt[{\mathrm{20}}]{{sin}\left({x}\right)\:\:\:}\:+\:\sqrt[{\mathrm{20}}]{{cos}\left({x}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:{R}_{\:{f}} \:=?\:\:\left({Range}\:\right) \\ $$$$ \\ $$

Question Number 167335 Answers: 2 Comments: 3

x_n =n∙sin(2πen!) Calculate lim_(n→∞) x_n

$$\mathrm{x}_{\mathrm{n}} =\mathrm{n}\centerdot\mathrm{sin}\left(\mathrm{2}\pi\mathrm{en}!\right) \\ $$$$\mathrm{Calculate} \\ $$$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}x}_{\mathrm{n}} \\ $$

Question Number 167334 Answers: 2 Comments: 0

b^b .2^b^b^2 = 4 ⇒b=?

$$\:\:\:\:{b}^{{b}} .\mathrm{2}^{{b}^{{b}^{\mathrm{2}} } } \:=\:\mathrm{4}\:\Rightarrow{b}=? \\ $$

Question Number 167332 Answers: 1 Comments: 0

lim_(n→∞) Σ_(k=1) ^n ((1/k))^k

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{\mathrm{1}}{{k}}\right)^{{k}} \\ $$

Question Number 167330 Answers: 2 Comments: 0

Calculate ∫(1/(x+(√(x^2 +x+1))))dx

$${Calculate} \\ $$$$\int\frac{\mathrm{1}}{{x}+\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}}{dx} \\ $$

Question Number 167328 Answers: 1 Comments: 0

∫_0 ^( π/2) ((cos x+cos^5 x sin x)/( (√(1+cos^2 x)))) dx =?

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:^{\mathrm{5}} {x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}}\:{dx}\:=? \\ $$

Question Number 167324 Answers: 2 Comments: 0

Question Number 167321 Answers: 0 Comments: 3

Question Number 167318 Answers: 1 Comments: 0

∫ (dx/( (√(x+(x)^(1/3) )))) =?

$$\:\:\:\:\:\:\int\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}+\sqrt[{\mathrm{3}}]{\mathrm{x}}}}\:=? \\ $$

Question Number 167312 Answers: 2 Comments: 1

∫ ((sin^3 x+1)/(sin^2 x−1)) dx =?

$$\:\:\:\:\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}\:\mathrm{dx}\:=? \\ $$

Question Number 167310 Answers: 0 Comments: 0

NICE CALCULUS ∫_0 ^1 ((ln(1−x)ln(1−(x/2)))/x)dx=?

$$\boldsymbol{\mathrm{NICE}}\:\boldsymbol{\mathrm{CALCULUS}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 167309 Answers: 0 Comments: 0

Question Number 167305 Answers: 1 Comments: 0

Q=∫ ((2sin (x))/( (√3) sin (x)−cos (x))) dx=?

$$\:\:\:{Q}=\int\:\frac{\mathrm{2sin}\:\left({x}\right)}{\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left({x}\right)−\mathrm{cos}\:\left({x}\right)}\:{dx}=? \\ $$

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