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Question Number 158228 Answers: 1 Comments: 0

∫((5x^3 −3x^2 +7x−3)/((x^2 +1)^2 ))dx Solve by first finding the partial fraction

$$\int\frac{\mathrm{5}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{3}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${Solve}\:{by}\:{first}\:{finding}\:{the}\:{partial} \\ $$$${fraction} \\ $$

Question Number 158209 Answers: 1 Comments: 0

Question Number 158207 Answers: 1 Comments: 0

Question Number 158205 Answers: 0 Comments: 0

(1) lim_(x→0) (((e^x −1)sin x+tan^3 x)/(arctan x ln (1+4x)+4arcsin^4 x)) (2) lim_(x→0) ((1−cos x+ln (1+tan^2 2x)+2arcsin^3 x)/(1−cos 4x+sin^2 x))

$$\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({e}^{{x}} −\mathrm{1}\right)\mathrm{sin}\:{x}+\mathrm{tan}\:^{\mathrm{3}} {x}}{\mathrm{arctan}\:{x}\:\mathrm{ln}\:\left(\mathrm{1}+\mathrm{4}{x}\right)+\mathrm{4arcsin}^{\mathrm{4}} \:{x}}\: \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}+\mathrm{ln}\:\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{2}{x}\right)+\mathrm{2arcsin}\:^{\mathrm{3}} \:{x}}{\mathrm{1}−\mathrm{cos}\:\mathrm{4}{x}+\mathrm{sin}\:^{\mathrm{2}} {x}} \\ $$

Question Number 158204 Answers: 2 Comments: 0

lim_(x→∞) (sin (√(x+1))−sin (√(x ))) =?

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{sin}\:\sqrt{{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}\:}\right)\:=? \\ $$

Question Number 158203 Answers: 0 Comments: 0

lim_(n→∞) Σ_(k=1) ^n (1/n).e^((2k+1)/k) =?

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{{n}}.{e}^{\frac{\mathrm{2}{k}+\mathrm{1}}{{k}}} \:=? \\ $$

Question Number 158190 Answers: 0 Comments: 1

∫((5x^3 −3x^2 +7x−3)/((x^2 +1)^2 ))dx Solve by first giving the partial functions

$$\int\frac{\mathrm{5}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{3}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx}\:{Solve}\:{by}\: \\ $$$${first}\:{giving}\:{the}\:{partial}\:{functions}\: \\ $$

Question Number 158176 Answers: 1 Comments: 0

∫{((x^2 −x−21)/(2x^3 −x^2 +8x−4))}dx

$$\int\left\{\frac{{x}^{\mathrm{2}} −{x}−\mathrm{21}}{\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{8}{x}−\mathrm{4}}\right\}{dx}\: \\ $$

Question Number 158175 Answers: 1 Comments: 1

lim_(x→+∞ ) ((sinx+x)/(3+2sinx))=?

$$\underset{{x}\rightarrow+\infty\:} {{lim}}\frac{{sinx}+{x}}{\mathrm{3}+\mathrm{2}{sinx}}=? \\ $$

Question Number 158173 Answers: 0 Comments: 0

simplify the expression (1+sin 𝛗)/(5+3tan 𝛗−4cos 𝛗) using small angles approximation up to the term containing φ^2

$$\mathrm{simplify}\:\mathrm{the}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{sin}\:\boldsymbol{\phi}\right)/\left(\mathrm{5}+\mathrm{3tan}\:\boldsymbol{\phi}−\mathrm{4cos}\:\boldsymbol{\phi}\right)\:\mathrm{using}\:\mathrm{small}\:\mathrm{angles}\:\mathrm{approximation}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{containing}\:\phi^{\mathrm{2}} \\ $$

Question Number 158166 Answers: 0 Comments: 1

If f((x/3))=((f(x))/2) and f(1−x)=1−f(x). find f(((173)/(1993))).

$$\:{If}\:{f}\left(\frac{{x}}{\mathrm{3}}\right)=\frac{{f}\left({x}\right)}{\mathrm{2}}\:{and}\:{f}\left(\mathrm{1}−{x}\right)=\mathrm{1}−{f}\left({x}\right). \\ $$$${find}\:{f}\left(\frac{\mathrm{173}}{\mathrm{1993}}\right). \\ $$

Question Number 158157 Answers: 0 Comments: 0

Question Number 158156 Answers: 1 Comments: 0

solve : ( x^( 2) +x −6)^( 3) + (7x^( 2) −9x −2)^( 3) −512(x^2 −x−1)^( 3) =0 x = ?

$$ \\ $$$$\:\:\:{solve}\:: \\ $$$$\left(\:{x}^{\:\mathrm{2}} +{x}\:−\mathrm{6}\right)^{\:\mathrm{3}} +\:\left(\mathrm{7}{x}^{\:\mathrm{2}} −\mathrm{9}{x}\:−\mathrm{2}\right)^{\:\mathrm{3}} −\mathrm{512}\left({x}^{\mathrm{2}} −{x}−\mathrm{1}\right)^{\:\mathrm{3}} =\mathrm{0} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:=\:? \\ $$$$ \\ $$

Question Number 158143 Answers: 1 Comments: 6

Question Number 158142 Answers: 0 Comments: 0

f(x)=x−[x] where [x] is the greatest integer function and −3≤x≤3 a) sketch f(x) b) state the domain of f(x) c) study the continuity of f(x) on its domain d) state the range of f(x)

$${f}\left({x}\right)={x}−\left[{x}\right]\:{where}\:\left[{x}\right]\:{is}\:{the}\:{greatest} \\ $$$${integer}\:{function}\:{and}\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{3} \\ $$$$\left.{a}\right)\:{sketch}\:{f}\left({x}\right) \\ $$$$\left.{b}\right)\:{state}\:{the}\:{domain}\:{of}\:{f}\left({x}\right) \\ $$$$\left.{c}\right)\:{study}\:{the}\:{continuity}\:{of}\:{f}\left({x}\right)\:{on}\:{its}\:{domain} \\ $$$$\left.{d}\right)\:{state}\:{the}\:{range}\:{of}\:{f}\left({x}\right) \\ $$

Question Number 158187 Answers: 1 Comments: 0

Solve for real numbers: { (((√x) - y^5 = 3)),(((((√x) - 3))^(1/5) - ((y^5 + 6))^(1/5) = - 1)) :}

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\sqrt{\mathrm{x}}\:-\:\mathrm{y}^{\mathrm{5}} \:=\:\mathrm{3}}\\{\sqrt[{\mathrm{5}}]{\sqrt{\mathrm{x}}\:-\:\mathrm{3}}\:-\:\sqrt[{\mathrm{5}}]{\mathrm{y}^{\mathrm{5}} \:+\:\mathrm{6}}\:=\:-\:\mathrm{1}}\end{cases}\: \\ $$$$ \\ $$

Question Number 158186 Answers: 1 Comments: 0

Question Number 158185 Answers: 0 Comments: 8

Question Number 158159 Answers: 2 Comments: 0

∫ (dx/(3−tan x)) =?

$$\:\:\:\:\:\:\int\:\frac{{dx}}{\mathrm{3}−\mathrm{tan}\:{x}}\:=? \\ $$

Question Number 158124 Answers: 1 Comments: 0

let 𝛚 be a root of the equation x^4 + (x - 1)^4 + 1 = 0 find 𝛀 = 𝛚^(300) + 𝛚^(301)

$$\mathrm{let}\:\boldsymbol{\omega}\:\mathrm{be}\:\mathrm{a}\:\mathrm{root}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\left(\mathrm{x}\:-\:\mathrm{1}\right)^{\mathrm{4}} \:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{find}\:\:\boldsymbol{\Omega}\:=\:\boldsymbol{\omega}^{\mathrm{300}} \:+\:\boldsymbol{\omega}^{\mathrm{301}} \\ $$

Question Number 158114 Answers: 2 Comments: 2

{ ((x^2 −3xy+2y^2 =35)),((x^2 +y^2 = 13)) :} ⇒x=? ∧ y=?

$$\:\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3}{xy}+\mathrm{2}{y}^{\mathrm{2}} =\mathrm{35}}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\:\mathrm{13}}\end{cases} \\ $$$$\:\Rightarrow{x}=?\:\wedge\:{y}=?\: \\ $$

Question Number 158191 Answers: 1 Comments: 1

Can we reach to (m/((m−1)s)) + ((m+1)/(ms^2 )) from ((ms+m(m+1))/(s(m−s))) ??

$${Can}\:{we}\:{reach}\:{to}\:\frac{{m}}{\left({m}−\mathrm{1}\right){s}}\:+\:\frac{{m}+\mathrm{1}}{{ms}^{\mathrm{2}} }\:{from}\: \\ $$$$ \\ $$$$\:\:\:\:\frac{{ms}+{m}\left({m}+\mathrm{1}\right)}{{s}\left({m}−{s}\right)}\:?? \\ $$

Question Number 158104 Answers: 1 Comments: 0

The comparison between Rahman and Aditya's books is 2: 3. If the number of their books is 20, then the number of Aditya's books is….

$$ \\ $$The comparison between Rahman and Aditya's books is 2: 3. If the number of their books is 20, then the number of Aditya's books is….

Question Number 158102 Answers: 0 Comments: 0

Given the quadrilateral. D.ABC Find the measure of the angle between AB and CD.

$$ \\ $$$$\mathrm{Given}\:\mathrm{the}\:\mathrm{quadrilateral}. \\ $$$$\mathrm{D}.\mathrm{ABC}\:\mathrm{Find}\:\mathrm{the}\:\mathrm{measure}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{AB}\:\mathrm{and}\:\mathrm{CD}. \\ $$

Question Number 158101 Answers: 1 Comments: 0

Find the image of points K (5,2) and L (1 5) after being reflected about the x axis.

$$ \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{image}\:\mathrm{of}\:\mathrm{points}\: \\ $$$$\mathrm{K}\:\left(\mathrm{5},\mathrm{2}\right)\:\mathrm{and}\:\mathrm{L}\:\left(\mathrm{1}\:\mathrm{5}\right)\:\mathrm{after}\: \\ $$$$\mathrm{being}\:\mathrm{reflected}\:\mathrm{about}\:\mathrm{the}\:\mathrm{x} \\ $$$$\mathrm{axis}. \\ $$

Question Number 158097 Answers: 2 Comments: 0

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