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Question Number 197843 Answers: 0 Comments: 1

Exercice 2

$$\boldsymbol{\mathrm{Exercice}}\:\:\mathrm{2} \\ $$

Question Number 197838 Answers: 1 Comments: 0

Question Number 197832 Answers: 1 Comments: 0

lim_(x→∞) ((2+(√(cosx)))/(−1+(√(cosx))))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{2}+\sqrt{{cosx}}}{−\mathrm{1}+\sqrt{{cosx}}}=? \\ $$

Question Number 197834 Answers: 1 Comments: 0

Question Number 197822 Answers: 1 Comments: 5

find maximum of ∣z^2 +2z−3∣ ?

$${find}\:{maximum}\:{of}\:\mid{z}^{\mathrm{2}} +\mathrm{2}{z}−\mathrm{3}\mid\:? \\ $$

Question Number 197821 Answers: 0 Comments: 0

find the value of : Ω = ∫_0 ^( 1) (( ln ( 1+ (1/x^( 2) ) ))/(2 + x^( 2) )) dx = ?

$$ \\ $$$$\:\:\:\:{find}\:{the}\:{value}\:\:{of}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:\mathrm{ln}\:\left(\:\mathrm{1}+\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:\right)}{\mathrm{2}\:+\:{x}^{\:\mathrm{2}} }\:{dx}\:=\:? \\ $$$$ \\ $$

Question Number 197820 Answers: 0 Comments: 0

Question Number 197819 Answers: 0 Comments: 0

find the value of : 𝛗 = Σ_(n=1) ^∞ (( (−1)^(n−1) H_( 2n) )/n) = ? where,H_n =1+(1/2) +(1/3) +...+(1/n)

$$ \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:{H}_{\:\mathrm{2}{n}} }{{n}}\:=\:? \\ $$$${where},{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+...+\frac{\mathrm{1}}{{n}} \\ $$

Question Number 197811 Answers: 0 Comments: 2

Question Number 197808 Answers: 1 Comments: 1

prove lim_(n→∞) x^n = 0 when ∣x∣ < 1

$${prove}\:\underset{{n}\rightarrow\infty} {{lim}}\:{x}^{{n}} \:=\:\mathrm{0}\:\:\:\:{when}\:\mid{x}\mid\:<\:\mathrm{1} \\ $$

Question Number 197805 Answers: 0 Comments: 0

Question Number 197802 Answers: 1 Comments: 0

I=∫_(−2) ^6 ((∣x−1∣)/(x−1)) dx =?

$$\:\:\:\mathrm{I}=\underset{−\mathrm{2}} {\overset{\mathrm{6}} {\int}}\:\frac{\mid\mathrm{x}−\mathrm{1}\mid}{\mathrm{x}−\mathrm{1}}\:\mathrm{dx}\:=? \\ $$

Question Number 197795 Answers: 3 Comments: 0

Question Number 197794 Answers: 1 Comments: 0

if x = log tan((π/4)+(y/2)), prove that y = −ilog tan(((ix)/2) + (π/4)) here i = (√(−1))

$$\:\:\:\:\mathrm{if}\:\mathrm{x}\:\:\:=\:\:\:\mathrm{log}\:\mathrm{tan}\left(\frac{\pi}{\mathrm{4}}+\frac{\mathrm{y}}{\mathrm{2}}\right),\:\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\mathrm{y}\:\:\:\:=\:\:\:−{i}\mathrm{log}\:\mathrm{tan}\left(\frac{{ix}}{\mathrm{2}}\:+\:\frac{\pi}{\mathrm{4}}\right)\:\:\:\:\:\mathrm{here}\:{i}\:\:=\:\sqrt{−\mathrm{1}} \\ $$

Question Number 197792 Answers: 2 Comments: 0

Solve the following differential equation 1) y′′ + y = e^x + x^3 , y(0)=2, y′(0)=0 2) y′′ + y^′ − 2y = x + sin2x, y(0)=1, y′(0)=0 3) y′′ − y′ = xe^x , y(0)=2, y′(0)= 1 Thank you

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{differential}\:\mathrm{equation} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{y}''\:+\:\mathrm{y}\:=\:\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{3}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{y}''\:+\:\mathrm{y}^{'} \:−\:\mathrm{2y}\:=\:\mathrm{x}\:+\:\mathrm{sin2x},\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{y}''\:−\:\mathrm{y}'\:=\:\mathrm{xe}^{\mathrm{x}} ,\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{y}'\left(\mathrm{0}\right)=\:\mathrm{1} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 197784 Answers: 1 Comments: 0

((x−2+3((x−3))^(1/3) (1+((x−3))^(1/3) )))^(1/3) + ((x+5+6((x−3))^(1/3) (1+2((x−3))^(1/3) )))^(1/3) = 5

$$\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}+\mathrm{3}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\left(\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\right)}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{5}+\mathrm{6}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\left(\mathrm{1}+\mathrm{2}\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{3}}\:\right)}\:=\:\mathrm{5} \\ $$

Question Number 197783 Answers: 2 Comments: 0

∫((x.arctg(x))/(x^2 +1))dx=?

$$\int\frac{{x}.\boldsymbol{{arctg}}\left(\boldsymbol{{x}}\right)}{\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{1}}\boldsymbol{{dx}}=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 197776 Answers: 1 Comments: 3

Question Number 197772 Answers: 1 Comments: 1

Can anyone do this? ∫^( +∞) _( 1) ((t−1)/((1+t)^3 lnt))dt

$$\mathrm{Can}\:\mathrm{anyone}\:\mathrm{do}\:\mathrm{this}? \\ $$$$\underset{\:\mathrm{1}} {\int}^{\:+\infty} \frac{\mathrm{t}−\mathrm{1}}{\left(\mathrm{1}+\mathrm{t}\right)^{\mathrm{3}} \:\mathrm{lnt}}\mathrm{dt} \\ $$

Question Number 197771 Answers: 1 Comments: 0

Question Number 197767 Answers: 0 Comments: 1

Question Number 197766 Answers: 1 Comments: 1

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

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

Question Number 197763 Answers: 0 Comments: 0

Question Number 197753 Answers: 3 Comments: 0

Solve the equation: (√(5x^2 +14x+9))−(√(x^2 −x−20))=5(√(x+1))

$${Solve}\:{the}\:{equation}: \\ $$$$\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{14}{x}+\mathrm{9}}−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{20}}=\mathrm{5}\sqrt{{x}+\mathrm{1}} \\ $$

Question Number 197752 Answers: 1 Comments: 0

find minimum value of m such that m^(19) = 1800 (mod 2029)

$$\:\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m} \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{m}^{\mathrm{19}} =\:\mathrm{1800}\:\left(\mathrm{mod}\:\mathrm{2029}\right) \\ $$

Question Number 197744 Answers: 1 Comments: 0

2∫_0 ^1 tan^(−1) x dx=?

$$\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} {x}\:{dx}=? \\ $$

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