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AllQuestion and Answers: Page 1229

Question Number 86298 Answers: 0 Comments: 5

let x^x^x^⋰ =2 x^2 =2 x=±(√2) then let x^x^x^⋰ =4 x^4 =4 x=±(4)^(1/4) =±(√2) so we had prove 2=4 right?

$${let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{2} \\ $$$${x}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}=\pm\sqrt{\mathrm{2}} \\ $$$${then}\:{let}\:{x}^{{x}^{{x}^{\iddots} } } =\mathrm{4} \\ $$$${x}^{\mathrm{4}} =\mathrm{4} \\ $$$${x}=\pm\sqrt[{\mathrm{4}}]{\mathrm{4}}=\pm\sqrt{\mathrm{2}} \\ $$$${so}\:{we}\:{had}\:{prove}\:\mathrm{2}=\mathrm{4}\:{right}? \\ $$

Question Number 86295 Answers: 0 Comments: 0

Question Number 86294 Answers: 1 Comments: 0

y = 2x + (y′)^2 −4y′

$$\mathrm{y}\:=\:\mathrm{2x}\:+\:\left(\mathrm{y}'\right)^{\mathrm{2}} −\mathrm{4y}' \\ $$

Question Number 86374 Answers: 0 Comments: 1

calculate bycomplex method ∫_1 ^(+∞) (dx/(1+x^2 ))

$${calculate}\:{bycomplex}\:{method}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 86282 Answers: 0 Comments: 7

Question Number 86288 Answers: 1 Comments: 0

∫ (dx/((1+x^4 )^(1/4) ))

$$\int\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{1}/\mathrm{4}} } \\ $$

Question Number 86269 Answers: 0 Comments: 1

∫((sec^2 (x))/((tan(x)−1)^4 (tan(x)−2))) dx

$$\int\frac{{sec}^{\mathrm{2}} \left({x}\right)}{\left({tan}\left({x}\right)−\mathrm{1}\right)^{\mathrm{4}} \left({tan}\left({x}\right)−\mathrm{2}\right)}\:{dx} \\ $$

Question Number 86254 Answers: 1 Comments: 0

∫ (√(x(√(x(√(x(√(x.......)))))))) dx

$$\int\:\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}.......}}}}\:\:\:\mathrm{dx} \\ $$

Question Number 86247 Answers: 0 Comments: 3

∫_0 ^8 ∫_0 ^x^(2/3) (√(x^2 +y^2 +1)) dy dx

$$\int_{\mathrm{0}} ^{\mathrm{8}} \int_{\mathrm{0}} ^{{x}^{\frac{\mathrm{2}}{\mathrm{3}}} } \:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}}\:{dy}\:{dx} \\ $$

Question Number 86246 Answers: 1 Comments: 0

∫((x^2 −1)/(x^2 +1)) (1/(√(1 + x^4 ))) dx = ?

$$\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx}\:=\:? \\ $$

Question Number 86244 Answers: 0 Comments: 0

Question Number 86242 Answers: 1 Comments: 0

Find y=CF+PI in following differential equation: (d^2 y/dx^2 )+3(dy/dx)+2y= e^(2x) sinx .

Question Number 86240 Answers: 1 Comments: 0

use the Chinese Remainder theorem to find x such that x ≡ 2(mod 3) 2x ≡ 3(mod 5) 3x≡ 4( mod 7)

$$\mathrm{use}\:\mathrm{the}\:\mathrm{Chinese}\:\mathrm{Remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{find} \\ $$$$\:\:{x}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}\:\equiv\:\mathrm{2}\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$$$\mathrm{2}{x}\:\equiv\:\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\:\mathrm{3}{x}\equiv\:\mathrm{4}\left(\:\mathrm{mod}\:\mathrm{7}\right) \\ $$

Question Number 86231 Answers: 2 Comments: 1

Question Number 86230 Answers: 1 Comments: 0

is (−1)^(m/n) =((((−1 )^m ))^(1/n) ) or =(((−1))^(1/n) )^m or both of them are fault and why ?

$${is}\:\:\left(−\mathrm{1}\right)^{\frac{{m}}{{n}}} \:=\left(\sqrt[{{n}}]{\left(−\mathrm{1}\:\right)^{{m}} }\right)\:{or}\:=\left(\sqrt[{{n}}]{−\mathrm{1}}\right)^{{m}} \\ $$$${or}\:{both}\:{of}\:{them}\:{are}\:{fault}\:{and}\:{why}\:? \\ $$

Question Number 86258 Answers: 1 Comments: 3

calculate I=∫_1 ^(+∞) ((x^2 −1)/(x^4 −x^2 +1))dx

$${calculate}\:{I}=\int_{\mathrm{1}} ^{+\infty} \frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 86256 Answers: 2 Comments: 0

Question Number 86260 Answers: 1 Comments: 1

Question Number 86214 Answers: 0 Comments: 8

Question Number 86206 Answers: 0 Comments: 3

1.line:y=−x+4 ,meets : xy=1 at:A,B. ⇒ S_(OA^△ B) =? (O=origin of cordinates) 2.find :center area of region bonded by corve: (√(x/a))+(√(y/b))=1,and x,y axes. (a≠b)∈R^+

Question Number 86204 Answers: 0 Comments: 0

lim_(x→0) ((x^2 sin ((1/x)) + x)/(((1+e))^(1/(x )) −e )) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:+\:\mathrm{x}}{\sqrt[{\mathrm{x}\:\:}]{\mathrm{1}+\mathrm{e}}\:−\mathrm{e}\:}\:? \\ $$

Question Number 86198 Answers: 0 Comments: 7

any methods to sketch these curves r = a(1−cosθ) r= a + b cosθ a>b r= a + bcosθ a<b

$$\mathrm{any}\:\mathrm{methods}\:\mathrm{to}\:\mathrm{sketch}\:\mathrm{these}\:\mathrm{curves} \\ $$$$\:\mathrm{r}\:=\:\mathrm{a}\left(\mathrm{1}−\mathrm{cos}\theta\right) \\ $$$$\:\mathrm{r}=\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{cos}\theta\:\:{a}>{b} \\ $$$$\:\mathrm{r}=\:\mathrm{a}\:+\:\mathrm{bcos}\theta\:\:\:{a}<{b} \\ $$

Question Number 86193 Answers: 1 Comments: 8

lim_(x→0) ((4x^2 +((6x^2 )/(√(9x^4 +9sin^2 x))))/(3x−((4x^3 −x)/(2x+1)))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4}{x}^{\mathrm{2}} +\frac{\mathrm{6}{x}^{\mathrm{2}} }{\sqrt{\mathrm{9}{x}^{\mathrm{4}} +\mathrm{9sin}\:^{\mathrm{2}} {x}}}}{\mathrm{3}{x}−\frac{\mathrm{4}{x}^{\mathrm{3}} −{x}}{\mathrm{2}{x}+\mathrm{1}}}\:=\:? \\ $$

Question Number 86189 Answers: 1 Comments: 0

Given that f(x)=((2x+7)/8) and g(x)= ((3x−6)/6), find (a) g(6), (b)f^(−1) (x) (c) the value of x if f(x)=g(x)

Question Number 86168 Answers: 1 Comments: 0

given sin x+sin y = 2sin (x+y) x+y ≠ 0 find the value of tan (x/2) tan (y/2) =

$$\mathrm{given}\: \\ $$$$\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{y}\:=\:\mathrm{2sin}\:\left(\mathrm{x}+\mathrm{y}\right)\: \\ $$$$\mathrm{x}+\mathrm{y}\:\neq\:\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{tan}\:\frac{\mathrm{x}}{\mathrm{2}}\:\mathrm{tan}\:\frac{\mathrm{y}}{\mathrm{2}}\:=\: \\ $$

Question Number 86167 Answers: 1 Comments: 3

∫_0 ^(π/2) ((arc tan ((√(tan x))))/(tan x)) dx

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{tan}\:\mathrm{x}}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\: \\ $$

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