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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

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

Question Number 86160 Answers: 1 Comments: 3

If (x−1) f(x) + f((1/x)) = (1/(x−1)) find f(x)

$$\mathrm{If}\:\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$

Question Number 86142 Answers: 2 Comments: 0

y′ .sin t cos t = y + sin^3 t y((π/4)) = 0

$$\mathrm{y}'\:.\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=\:\mathrm{y}\:+\:\mathrm{sin}\:^{\mathrm{3}} \mathrm{t}\: \\ $$$$\mathrm{y}\left(\frac{\pi}{\mathrm{4}}\right)\:=\:\mathrm{0}\: \\ $$

Question Number 86141 Answers: 0 Comments: 5

A number n leaves a remainder of 22 when divided by 24 and remainder 30 when divided by 33. Find the least possible value of n

$$\mathrm{A}\:\mathrm{number}\:\mathrm{n}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{22}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{remainder}\:\:\mathrm{30}\:\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{33}.\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{possible} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\mathrm{n} \\ $$

Question Number 86140 Answers: 0 Comments: 1

Question Number 86138 Answers: 1 Comments: 1

∫ _(−4) ^8 ((∣x∣)/x) dx = ?

$$\int\underset{−\mathrm{4}} {\overset{\mathrm{8}} {\:}}\:\frac{\mid\mathrm{x}\mid}{\mathrm{x}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 86132 Answers: 1 Comments: 0

∫x^3 sin(2x^2 +6)^5 dx

$$\int{x}^{\mathrm{3}} \:{sin}\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}\right)^{\mathrm{5}} \:{dx} \\ $$

Question Number 86129 Answers: 0 Comments: 1

Given that f(x)=8x and g(x)=((3x−2)/4), find (a) f^(−1) (x) (b) an expression for fg(x) (c) value of x which fg(x)=20

$${Given}\:{that}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{8}\boldsymbol{\mathrm{x}}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\frac{\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{2}}{\mathrm{4}},\:{find} \\ $$$$\left(\mathrm{a}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\mathrm{b}\right)\:{an}\:{expression}\:{for}\:\boldsymbol{{fg}}\left(\boldsymbol{\mathrm{x}}\right) \\ $$$$\left(\mathrm{c}\right)\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{20}\: \\ $$

Question Number 86128 Answers: 1 Comments: 0

⌊2x−(1/2)⌋=⌊∣x∣−(1/2)⌋=2x−2

$$\lfloor\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\lfloor\mid{x}\mid−\frac{\mathrm{1}}{\mathrm{2}}\rfloor=\mathrm{2}{x}−\mathrm{2} \\ $$

Question Number 86116 Answers: 0 Comments: 1

lim_(x→∞) ((tanx)/x)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{tanx}}{{x}} \\ $$

Question Number 86113 Answers: 0 Comments: 5

(1)Determine the following if it is convergent or divergent Σ_(n=1) ^∞ ((sin(n))/n) (2)Σ_(n=1) ^∞ ((sin(n^p ))/n^p ), pεR,find the range of p when it is convergent

$$\left(\mathrm{1}\right){Determine}\:{the}\:{following} \\ $$$${if}\:{it}\:{is}\:{convergent}\:{or}\:{divergent} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}^{{p}} \right)}{{n}^{{p}} },\:{p}\epsilon\mathbb{R},{find}\:{the}\:{range}\: \\ $$$${of}\:{p}\:{when}\:{it}\:{is}\:{convergent} \\ $$

Question Number 86111 Answers: 2 Comments: 1

sin (((3π)/2)cos x) = −(1/2)

$$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 86094 Answers: 1 Comments: 1

2∫(√(x^3 +4)) dx

$$\mathrm{2}\int\sqrt{{x}^{\mathrm{3}} +\mathrm{4}}\:{dx} \\ $$

Question Number 86092 Answers: 1 Comments: 1

∫(1/(√(5−4x−2x^2 )))dx

$$\int\frac{\mathrm{1}}{\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 86091 Answers: 1 Comments: 1

∫ ((sin x−cos x)/(√(sin 2x))) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx} \\ $$

Question Number 86088 Answers: 0 Comments: 5

Find the sum of the series below: 1+2+3−4−5−6+7+8+9−10−11−12+13+14+15...−3020

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}−\mathrm{4}−\mathrm{5}−\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}−\mathrm{10}−\mathrm{11}−\mathrm{12}+\mathrm{13}+\mathrm{14}+\mathrm{15}...−\mathrm{3020} \\ $$

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