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AllQuestion and Answers: Page 114

Question Number 212171 Answers: 0 Comments: 0

Question Number 212170 Answers: 2 Comments: 4

Question Number 212169 Answers: 1 Comments: 0

lim_(λ→0^+ ) ∫_λ ^(2λ) (e^((x−1)^2 ) /x)dx = ?

$$\:\:\:\:\:\:\:\:\:\:\underset{\lambda\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\int_{\lambda} ^{\mathrm{2}\lambda} \:\frac{{e}^{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } }{{x}}{dx}\:=\:? \\ $$

Question Number 212164 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (( (−1)^n )/(3n+1)) − ln((2)^(1/3) ) = ?

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{{n}} }{\mathrm{3}{n}+\mathrm{1}}\:−\:\mathrm{ln}\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}\:\right)\:=\:? \\ $$$$\: \\ $$$$ \\ $$

Question Number 212159 Answers: 1 Comments: 0

Question Number 212160 Answers: 1 Comments: 0

Question Number 212152 Answers: 2 Comments: 0

Question Number 212168 Answers: 0 Comments: 0

Question Number 212146 Answers: 2 Comments: 0

Find maximum without derivative x(6−x)(x−3)^2 (3<x<6)

$$\mathrm{Find}\:\mathrm{maximum}\:\mathrm{without}\:\mathrm{derivative} \\ $$$${x}\left(\mathrm{6}−{x}\right)\left({x}−\mathrm{3}\right)^{\mathrm{2}} \:\left(\mathrm{3}<{x}<\mathrm{6}\right) \\ $$

Question Number 212141 Answers: 2 Comments: 0

∫((cos^2 x)/(sin x+cos x))dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\int\frac{\mathrm{cos}^{\mathrm{2}} {x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{dx}. \\ $$$$ \\ $$

Question Number 212140 Answers: 1 Comments: 0

If, f(x)=− x^2 +4x −3 , g(x)= { (( (√(7−x)) 0≤x <7)),(( ⌊ 5x ⌋ −5x x≥7)) :} ⇒ R_(fog) = (a ,b] find the value of b−a R_(fog) = { (fog)(x)∣ x∈ D_(fog) }

$$ \\ $$$$\:\mathrm{I}{f},\:\:\:\:\:{f}\left({x}\right)=−\:{x}^{\mathrm{2}} \:+\mathrm{4}{x}\:−\mathrm{3}\: \\ $$$$\:\:\:\:\: \\ $$$$,\:{g}\left({x}\right)=\:\begin{cases}{\:\sqrt{\mathrm{7}−{x}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\:<\mathrm{7}}\\{\:\:\lfloor\:\mathrm{5}{x}\:\rfloor\:−\mathrm{5}{x}\:\:\:\:\:\:\:\:{x}\geqslant\mathrm{7}}\end{cases}\:\:\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\:\:{R}_{{fog}} \:=\:\left({a}\:,{b}\right]\:\: \\ $$$$\:\:\:\:\:\:\:{find}\:\:{the}\:{value}\:{of}\:\:\:{b}−{a} \\ $$$$\:\:\:\:\:\:{R}_{{fog}} \:=\:\left\{\:\left({fog}\right)\left({x}\right)\mid\:{x}\in\:{D}_{{fog}} \:\right\} \\ $$

Question Number 212139 Answers: 1 Comments: 0

I_n = ∫_(−π) ^( π) (( sin(nx ))/((1 + e^x )sinx)) dx =?

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{I}_{{n}} \:=\:\int_{−\pi} ^{\:\pi} \frac{\:\mathrm{sin}\left({nx}\:\right)}{\left(\mathrm{1}\:+\:{e}^{{x}} \right)\mathrm{sin}{x}}\:{dx}\:=?\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 212137 Answers: 1 Comments: 0

lim_(n→∞) ((n)^(1/n) −1)(√n)=?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{{n}}]{{n}}−\mathrm{1}\right)\sqrt{{n}}=? \\ $$$$ \\ $$

Question Number 212136 Answers: 0 Comments: 0

what is the maximal number of consecutive natural numbers which are coprime with the sum of their divisors

$${what}\:{is}\:{the}\:{maximal}\:{number}\:{of}\:{consecutive}\:{natural} \\ $$$${numbers}\:{which}\:{are}\:{coprime}\:{with}\:{the} \\ $$$${sum}\:{of}\:{their}\:{divisors} \\ $$

Question Number 212131 Answers: 0 Comments: 0

Question Number 212130 Answers: 2 Comments: 0

Find: AD : BC = ? AP = 2, BP = 3, PC = 4, PD = 5 Help me please.

$$\:\:\: \\ $$$$ {Find}:\:\:{AD}\::\:{BC}\:=\:? \\ $$$$\:\:\:{AP}\:=\:\mathrm{2},\:\:\:{BP}\:=\:\mathrm{3},\:\:\:{PC}\:=\:\mathrm{4},\:\:\:{PD}\:=\:\mathrm{5} \\ $$$$\:\:\:\mathbb{H}{elp}\:\:{me}\:\:{please}. \\ $$

Question Number 212123 Answers: 1 Comments: 0

solve an equation: (√(ln x))=ln(√x)

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{an}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\boldsymbol{\mathrm{ln}}\:\boldsymbol{{x}}}=\boldsymbol{\mathrm{ln}}\sqrt{\boldsymbol{{x}}} \\ $$

Question Number 212114 Answers: 4 Comments: 0

(x^2 + 1)(y^2 + 1) + 9 = 6(x+y) Find that: x^2 + y^2 = ?

$$ \\ $$$$\:\:\:\left({x}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left({y}^{\mathrm{2}} \:+\:\mathrm{1}\right)\:+\:\mathrm{9}\:=\:\mathrm{6}\left({x}+{y}\right) \\ $$$$\:\:\:\mathcal{F}{ind}\:{that}:\:\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:=\:? \\ $$$$ \\ $$

Question Number 212108 Answers: 1 Comments: 0

∫_( −1) ^( 1) ∣ x ∣ ∙ ln(x^2 − x + 1) dx = ? Help me, please

$$ \\ $$$$\:\:\:\int_{\:−\mathrm{1}} ^{\:\:\mathrm{1}} \mid\:{x}\:\mid\:\centerdot\:{ln}\left({x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{1}\right)\:{dx}\:=\:? \\ $$$$\:\:\:\mathcal{H}{elp}\:{me},\:{please} \\ $$$$ \\ $$

Question Number 212101 Answers: 0 Comments: 0

Question Number 212099 Answers: 3 Comments: 0

Question Number 212098 Answers: 1 Comments: 0

Prove that ln (((√(13))−1)/(10)) + (√(13)) − 2 >0 without calculator.

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{ln}\:\frac{\sqrt{\mathrm{13}}−\mathrm{1}}{\mathrm{10}}\:+\:\sqrt{\mathrm{13}}\:−\:\mathrm{2}\:>\mathrm{0} \\ $$$$\mathrm{without}\:\mathrm{calculator}. \\ $$

Question Number 212097 Answers: 1 Comments: 0

lim_(x→0) (x^2 +e^x )^(1/x) =?

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

Question Number 212107 Answers: 1 Comments: 0

I=∫_0 ^∞ ((x cos x−sin x)/x^2 )dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{I}=\int_{\mathrm{0}} ^{\infty} \frac{{x}\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} }{dx}. \\ $$$$ \\ $$

Question Number 212094 Answers: 1 Comments: 0

[1+(1/( (√2)))+(1/( (√3)))+(1/( (√4)))+.......+(1/( (√(1000000))))]=? note: [6.25]=6 ,[0.47]=0

$$\left[\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+.......+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1000000}}}\right]=? \\ $$$$\boldsymbol{{note}}:\:\:\:\left[\mathrm{6}.\mathrm{25}\right]=\mathrm{6}\:\:\:,\left[\mathrm{0}.\mathrm{47}\right]=\mathrm{0} \\ $$

Question Number 212085 Answers: 1 Comments: 1

a,b,c ∈ N 5a + 6b + 7c = 70 find: max(a) = ?

$$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\:\mathbb{N} \\ $$$$\mathrm{5a}\:+\:\mathrm{6b}\:+\:\mathrm{7c}\:=\:\mathrm{70} \\ $$$$\mathrm{find}:\:\:\mathrm{max}\left(\mathrm{a}\right)\:=\:? \\ $$

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