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Question Number 85554    Answers: 0   Comments: 1

2x^2 +5x+7=0

$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$

Question Number 85551    Answers: 0   Comments: 1

∫ (dx/(x^2 (x^4 +1)^(3/4) ))

$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$

Question Number 85546    Answers: 0   Comments: 1

Question Number 85542    Answers: 1   Comments: 4

Question Number 85540    Answers: 1   Comments: 0

find the range y=((x+[x])/(1−[x]+x))

$${find}\:{the}\:{range} \\ $$$${y}=\frac{{x}+\left[{x}\right]}{\mathrm{1}−\left[{x}\right]+{x}} \\ $$

Question Number 85535    Answers: 0   Comments: 0

Question Number 85534    Answers: 1   Comments: 2

Question Number 85532    Answers: 1   Comments: 0

Find the term independent of x in the expression of (2x−(1/(2x)))^9

$${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$

Question Number 85523    Answers: 1   Comments: 1

Question Number 85589    Answers: 0   Comments: 0

∫((1+4u)/(−4u^2 +2u+2))du

$$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$

Question Number 85503    Answers: 1   Comments: 0

(dy/dx) = sec (x+y)

$$\frac{{dy}}{{dx}}\:=\:\mathrm{sec}\:\left({x}+{y}\right)\: \\ $$

Question Number 85500    Answers: 1   Comments: 0

The function of f and g are defined by f:g→(x/(bx−2)), x ≠ (2/b) and b ≠ 0, where a and b are real numbers g:x →2x−11 (a) If f(2)= ((-1)/2) and f^(−1) (1) = -1, find a and b and write down the expression for f in terms of x (b) Find the value of x for which fg(x)= ((-1)/2)

$${The}\:{function}\:{of}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{g}}\rightarrow\frac{{x}}{\boldsymbol{\mathrm{b}}{x}−\mathrm{2}},\:{x}\:\neq\:\frac{\mathrm{2}}{\boldsymbol{\mathrm{b}}}\:{and}\:\boldsymbol{\mathrm{b}}\:\neq\:\mathrm{0},\:{where}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{are}\:{real}\:{numbers}\:\boldsymbol{\mathrm{g}}:\boldsymbol{\mathrm{x}}\:\rightarrow\mathrm{2}{x}−\mathrm{11} \\ $$$$\left({a}\right)\:{If}\:\boldsymbol{\mathrm{f}}\left(\mathrm{2}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}}\:{and}\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\mathrm{1}\right)\:=\:-\mathrm{1},\:{find}\:\boldsymbol{\mathrm{a}}\:{and}\:\boldsymbol{\mathrm{b}}\:{and}\:{write}\:{down}\:{the}\:{expression}\:{for}\:\boldsymbol{\mathrm{f}}\:{in}\:{terms}\:{of}\:\boldsymbol{\mathrm{x}} \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{F}}{ind}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{x}}\:{for}\:{which}\:\boldsymbol{\mathrm{fg}}\left(\boldsymbol{\mathrm{x}}\right)=\:\frac{-\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 85498    Answers: 1   Comments: 1

(1−x^2 )(dy/(dx ))−2xy=0

$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}\:}−\mathrm{2}{xy}=\mathrm{0} \\ $$

Question Number 85490    Answers: 0   Comments: 3

Given that the expression 2x^3 +px^2 −8x+9 is exactly divisable by x^2 −6x+5, find the value of p and q. Hence factorise the expression fully

$${Given}\:{that}\:{the}\:{expression}\:\mathrm{2}{x}^{\mathrm{3}} +{px}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{9}\:{is}\:{exactly}\:{divisable}\:{by}\:{x}^{\mathrm{2}} −\mathrm{6}{x}+\mathrm{5},\:{find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{q}}.\:{Hence}\:{factorise}\:{the}\:{expression}\:{fully} \\ $$

Question Number 85489    Answers: 0   Comments: 2

Find all angles between 0° and 360°, for which 8sinθ=3cos^2 θ

$${Find}\:{all}\:{angles}\:{between}\:\mathrm{0}°\:{and}\:\mathrm{360}°,\:{for}\:{which}\:\mathrm{8}{sin}\theta=\mathrm{3}{cos}^{\mathrm{2}} \theta \\ $$

Question Number 85488    Answers: 1   Comments: 0

∫ (dx/((x^4 +x^2 +1)^(3/4) ))

$$\int\:\frac{{dx}}{\left({x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$

Question Number 85484    Answers: 1   Comments: 0

show that (1/(secθ+1))+(1/(secθ−1))≡2cosecθcotθ

$${show}\:{that}\:\frac{\mathrm{1}}{{sec}\theta+\mathrm{1}}+\frac{\mathrm{1}}{{sec}\theta−\mathrm{1}}\equiv\mathrm{2}{cosec}\theta{cot}\theta \\ $$

Question Number 85480    Answers: 1   Comments: 0

∫((csc(x))/(cos(x)+cos^3 (x)+...+cos^(2n+1) (x)))dx ∀x∈n

$$\int\frac{{csc}\left({x}\right)}{{cos}\left({x}\right)+{cos}^{\mathrm{3}} \left({x}\right)+...+{cos}^{\mathrm{2}{n}+\mathrm{1}} \left({x}\right)}{dx} \\ $$$$\forall{x}\in{n} \\ $$

Question Number 85472    Answers: 1   Comments: 4

Question Number 85513    Answers: 1   Comments: 0

Solve the following equation: ((dy/dx))^2 +2y cot x (dy/dx) = y^2

$$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\:\left(\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\right)^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{cot}}\:\boldsymbol{\mathrm{x}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:=\:\boldsymbol{\mathrm{y}}^{\mathrm{2}} \\ $$

Question Number 85468    Answers: 1   Comments: 0

∫ln(1−e^x ) dx

$$\int{ln}\left(\mathrm{1}−{e}^{{x}} \right)\:{dx} \\ $$

Question Number 85462    Answers: 0   Comments: 0

Question Number 85456    Answers: 0   Comments: 7

∫ (√(csc x )) dx?

$$\int\:\sqrt{\mathrm{csc}\:\mathrm{x}\:}\:\mathrm{dx}? \\ $$

Question Number 85447    Answers: 1   Comments: 5

Question Number 85442    Answers: 1   Comments: 1

Question Number 85441    Answers: 1   Comments: 0

∫ ((6x^4 −4)/(√(x^4 −2))) dx = ?

$$\int\:\frac{\mathrm{6x}^{\mathrm{4}} −\mathrm{4}}{\sqrt{\mathrm{x}^{\mathrm{4}} −\mathrm{2}}}\:\mathrm{dx}\:=\:? \\ $$

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