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AllQuestion and Answers: Page 366

Question Number 184302 Answers: 1 Comments: 0

Question Number 184287 Answers: 2 Comments: 0

If the area enclosed between the curves y=x² and the line y = 2x is rotated round the x-axis through 4 right angles, find the volume of the solid generated

Question Number 184280 Answers: 1 Comments: 13

Given { ((a_0 =1)),((a_(n+1) =(1/2)(3a_n +(√(5a_n ^2 −4)) ))) :} ∀n≥0 , n∈I find a_n .

$$\:\:{Given}\:\begin{cases}{{a}_{\mathrm{0}} =\mathrm{1}}\\{{a}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}{a}_{{n}} +\sqrt{\mathrm{5}{a}_{{n}} ^{\mathrm{2}} −\mathrm{4}}\:\right)}\end{cases} \\ $$$$\:\forall{n}\geqslant\mathrm{0}\:,\:{n}\in{I}\: \\ $$$$\:\:{find}\:{a}_{{n}} . \\ $$

Question Number 184270 Answers: 2 Comments: 0

((−64))^(1/6) ∙((−128))^(1/7) =?

$$\sqrt[{\mathrm{6}}]{−\mathrm{64}}\centerdot\sqrt[{\mathrm{7}}]{−\mathrm{128}}=? \\ $$

Question Number 184264 Answers: 1 Comments: 0

Question Number 184260 Answers: 3 Comments: 0

x+(1/x)=−1 x^(1377) =?

$$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=−\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{1377}} =? \\ $$

Question Number 184258 Answers: 2 Comments: 0

2yz−4z+2x−2=0 2xz−2z+2y−4=0 2xy−4x−2y+2z+4=0 how to find the all values of the (x,y,z) ?

$$\:\:\:\mathrm{2yz}−\mathrm{4z}+\mathrm{2x}−\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xz}−\mathrm{2z}+\mathrm{2y}−\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{2xy}−\mathrm{4x}−\mathrm{2y}+\mathrm{2z}+\mathrm{4}=\mathrm{0} \\ $$$$\:\:\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\mathrm{the}\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:? \\ $$

Question Number 184251 Answers: 6 Comments: 0

If x (√y) = 2904 Find: y=?

$$\mathrm{If}\:\:\:\mathrm{x}\:\sqrt{\mathrm{y}}\:=\:\mathrm{2904} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{y}=? \\ $$

Question Number 184242 Answers: 1 Comments: 0

Question Number 184240 Answers: 2 Comments: 1

Question Number 184239 Answers: 1 Comments: 0

f(x)= { ((x−2 if x>3)),((3 if x=3)),((−x+4 if 1≤x<3)),((1 if 1<x)) :} faind lim_(x→1) f(x)=? and lim_(x→3) f(x)=?

$${f}\left({x}\right)=\begin{cases}{{x}−\mathrm{2}\:\:\:\:\:\:\:{if}\:\:{x}>\mathrm{3}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:{x}=\mathrm{3}}\\{−{x}+\mathrm{4}\:\:\:\:{if}\:\:\mathrm{1}\leqslant{x}<\mathrm{3}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:\mathrm{1}<{x}}\end{cases} \\ $$$${faind}\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=?\:\:{and}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$

Question Number 184628 Answers: 0 Comments: 0

Question Number 184626 Answers: 1 Comments: 0

∫_0 ^(+oo) ((artan(2x)−arctan(x))/x)dx

$$\int_{\mathrm{0}} ^{+{oo}} \:\frac{{artan}\left(\mathrm{2}{x}\right)−{arctan}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 184629 Answers: 0 Comments: 0

Question Number 184223 Answers: 0 Comments: 2

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Question Number 184218 Answers: 1 Comments: 0

Question Number 184199 Answers: 1 Comments: 1

Question Number 184188 Answers: 1 Comments: 0

Differentiate, y = x^(x−1) hi

$$\mathrm{Differentiate},\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{x}−\mathrm{1}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{hi} \\ $$

Question Number 184187 Answers: 1 Comments: 0

Differentiate, y=e^x + x^x M.m

$$\mathrm{Differentiate},\:\mathrm{y}=\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{x}^{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 184185 Answers: 1 Comments: 0

Differentiate, y=(log_e x)^x M.m

$$\mathrm{Differentiate},\:\mathrm{y}=\left(\mathrm{log}_{\mathrm{e}} \mathrm{x}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{M}.\mathrm{m} \\ $$

Question Number 184183 Answers: 0 Comments: 0

Question Number 184184 Answers: 1 Comments: 0

y=(sinx)^x Differentiate

$$\mathrm{y}=\left(\mathrm{sinx}\right)^{\mathrm{x}} \\ $$$$ \\ $$$$\mathrm{Differentiate} \\ $$

Question Number 184175 Answers: 2 Comments: 0

Question Number 184160 Answers: 4 Comments: 1

Given { ((a_0 =1)),((a_(n+1) =(1/2)(3a_n +(√(5a_n ^2 −4)) ))) :} ∀n≥0 , n∈I find a_n .

Question Number 184159 Answers: 1 Comments: 1

prove that 0^0 =1

$${prove}\:{that}\:\mathrm{0}^{\mathrm{0}} =\mathrm{1} \\ $$

Question Number 184144 Answers: 2 Comments: 0

𝚺_(n=1) ^∞ 𝚺_(m=1) ^∞ (((−1)^(n+m) )/(nm(n+m)))

$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\underset{\boldsymbol{\mathrm{m}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{m}}} }{\boldsymbol{\mathrm{nm}}\left(\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{m}}\right)} \\ $$

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