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Question Number 11475    Answers: 2   Comments: 0

Question Number 11474    Answers: 1   Comments: 0

Question Number 11473    Answers: 1   Comments: 1

Show that the graph of y = x^3 + 2x^2 + x + 1 , between x = − 1 and x = 2 lies entirely above the x − axis

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:,\:\mathrm{between}\:\mathrm{x}\:=\:−\:\mathrm{1}\:\mathrm{and}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{lies}\:\mathrm{entirely}\:\mathrm{above}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis} \\ $$

Question Number 11459    Answers: 2   Comments: 0

If ((4x^2 −4xy+3y^2 )/(2y^2 +2xy−5x^2 ))=1 if the ((x+y)/(x−y)) what is th value?

$$\boldsymbol{\mathrm{If}} \\ $$$$\frac{\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{xy}}+\mathrm{3}\boldsymbol{\mathrm{y}}^{\mathrm{2}} }{\mathrm{2}\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{xy}}−\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} }=\mathrm{1}\:\:\boldsymbol{\mathrm{if}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\frac{\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{y}}}\:\:\boldsymbol{\mathrm{what}}\:\:\boldsymbol{\mathrm{is}}\:\:\boldsymbol{\mathrm{th}}\:\:\boldsymbol{\mathrm{value}}? \\ $$

Question Number 11456    Answers: 2   Comments: 3

sin x − cos x = a, (π/4) ≤ x ≤ (π/2) Which statement is correct? (1) sin^2 x − cos^2 x = −(1/2)(√(3 + 2a^2 − a^4 )) (2) sin^4 x + cos^4 x = (1/8)(−3a^4 + 6a^2 + 5) (3) sin 2x = ((1 − a^2 )/2) (4) tan^2 x + cot^2 x = ((−3a^4 − 2a^2 + 8a + 13 )/(2(a^4 + 2a^2 + 1)))

$$\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:{a},\:\:\frac{\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{Which}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}\:+\:\mathrm{2}{a}^{\mathrm{2}} \:−\:{a}^{\mathrm{4}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}^{\mathrm{4}} \:{x}\:+\:\mathrm{cos}^{\mathrm{4}} \:{x}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{3}{a}^{\mathrm{4}} \:+\:\mathrm{6}{a}^{\mathrm{2}} \:+\:\mathrm{5}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:−\:{a}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{tan}^{\mathrm{2}} \:{x}\:+\:\mathrm{cot}^{\mathrm{2}} \:{x}\:=\:\frac{−\mathrm{3}{a}^{\mathrm{4}} \:−\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{8}{a}\:+\:\mathrm{13}\:}{\mathrm{2}\left({a}^{\mathrm{4}} \:+\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{1}\right)} \\ $$

Question Number 11453    Answers: 0   Comments: 0

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Question Number 11444    Answers: 2   Comments: 0

If lim_(x→0) (((√(px + q)) − 2)/x) = 1 What is the value of p + q ?

$$\mathrm{If}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{px}\:+\:{q}}\:−\:\mathrm{2}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{p}\:+\:{q}\:? \\ $$

Question Number 11436    Answers: 0   Comments: 1

∫_0 ^(𝛑/4) sinx×cos^7 x dx. solves...

$$ \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\boldsymbol{\pi}}{\mathrm{4}}} {\int}}\boldsymbol{\mathrm{sinx}}×\boldsymbol{\mathrm{cos}}^{\mathrm{7}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}. \\ $$$$\boldsymbol{\mathrm{solves}}... \\ $$

Question Number 11433    Answers: 1   Comments: 5

for r=(1/θ), show that the arc length between θ=3π^(−1) and θ=nπ^(−1) (where n>3) is aproxiately equal to the length of the line y=3π^(−1) between the same bounds. Or show otherwise.

$$\mathrm{for}\:{r}=\frac{\mathrm{1}}{\theta},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{between} \\ $$$$\theta=\mathrm{3}\pi^{−\mathrm{1}} \:\:\mathrm{and}\:\theta={n}\pi^{−\mathrm{1}} \:\:\:\left(\mathrm{where}\:\:{n}>\mathrm{3}\right)\:\:\mathrm{is}\:\mathrm{aproxiately} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:{y}=\mathrm{3}\pi^{−\mathrm{1}} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{same}\:\mathrm{bounds}.\:\mathrm{Or}\:\mathrm{show}\:\mathrm{otherwise}. \\ $$$$ \\ $$

Question Number 11429    Answers: 1   Comments: 0

∫_0 ^3 ((2x+3)/(2x+1))dx=𝛂+ln7. 𝛂=? please......

$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}}{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}}\boldsymbol{\mathrm{dx}}=\boldsymbol{\alpha}+\boldsymbol{\mathrm{ln}}\mathrm{7}. \\ $$$$\boldsymbol{\alpha}=? \\ $$$$\boldsymbol{\mathrm{please}}...... \\ $$

Question Number 11425    Answers: 1   Comments: 0

Question Number 11423    Answers: 0   Comments: 0

please solve. ax^4 + bx^3 + cx^2 + dx + e = 0

$$\mathrm{please}\:\mathrm{solve}.\: \\ $$$$\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{e}\:=\:\mathrm{0} \\ $$

Question Number 11420    Answers: 2   Comments: 1

please ∫_0 ^∞ ((xlogx)/((1+x^2 )^2 ))dx=

$${please} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{xlogx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}= \\ $$

Question Number 11419    Answers: 0   Comments: 1

If A = {whole numbers} and B={natural numbers}, then A△B=___.

$$\mathrm{If}\:\mathrm{A}\:=\:\left\{\mathrm{whole}\:\mathrm{numbers}\right\}\:\mathrm{and}\: \\ $$$$\mathrm{B}=\left\{\mathrm{natural}\:\mathrm{numbers}\right\},\:\mathrm{then}\:\mathrm{A}\bigtriangleup\mathrm{B}=\_\_\_. \\ $$

Question Number 11417    Answers: 0   Comments: 0

A = log (5x + 1)(3x + 5) B = (1/(log (5x+ 1)(x − 1))) If A + B ≥ 1, x must be ...

$${A}\:=\:\mathrm{log}\:\left(\mathrm{5}{x}\:+\:\mathrm{1}\right)\left(\mathrm{3}{x}\:+\:\mathrm{5}\right) \\ $$$${B}\:=\:\frac{\mathrm{1}}{\mathrm{log}\:\left(\mathrm{5}{x}+\:\mathrm{1}\right)\left({x}\:−\:\mathrm{1}\right)} \\ $$$$\mathrm{If}\:{A}\:+\:{B}\:\geqslant\:\mathrm{1},\:{x}\:\mathrm{must}\:\mathrm{be}\:... \\ $$

Question Number 11416    Answers: 1   Comments: 0

Question Number 11413    Answers: 1   Comments: 0

Find the length of the arc of the hyperbolic spiral rθ=a lying between r=a and r=2a.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolic} \\ $$$$\mathrm{spiral}\:\:\mathrm{r}\theta=\mathrm{a}\:\:\mathrm{lying}\:\mathrm{between}\:\:\mathrm{r}=\mathrm{a}\:\:\mathrm{and}\: \\ $$$$\mathrm{r}=\mathrm{2a}. \\ $$

Question Number 11408    Answers: 1   Comments: 0

Question Number 11406    Answers: 1   Comments: 0

Evaluate: ∫_( 1) ^( 3) ((x − 1)/((x + 1)^2 )) dx

$$\mathrm{Evaluate}:\:\:\:\:\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{3}} \:\:\frac{\mathrm{x}\:−\:\mathrm{1}}{\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 11405    Answers: 1   Comments: 0

Find the magnitude of two forces such that if they act at right angle their resultant is (√(10)) , and (√(13)) if they act at an angle of 60°.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{such}\:\mathrm{that}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{their} \\ $$$$\mathrm{resultant}\:\mathrm{is}\:\sqrt{\mathrm{10}}\:,\:\mathrm{and}\:\sqrt{\mathrm{13}}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°.\: \\ $$

Question Number 11403    Answers: 0   Comments: 1

how can demonstred that cos(2x)−sin(2x)−1=−cos^2 x

$${how}\:{can}\:{demonstred}\:{that}\: \\ $$$${cos}\left(\mathrm{2}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{1}=−{cos}^{\mathrm{2}} {x} \\ $$

Question Number 11399    Answers: 1   Comments: 0

The sum of the first and last term of an A.P is 51. And the sum of the progression is 255. Find the last term of the A.P.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}\:\mathrm{is}\:\mathrm{51}.\:\mathrm{And}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{progression}\:\mathrm{is}\:\mathrm{255}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$

Question Number 11398    Answers: 0   Comments: 0

Solve for x : 625^(x − 5) = 200(√x^3 )

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\sqrt{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 11395    Answers: 0   Comments: 1

Prove that those functions below don′t have limit a) lim_((x,y)→(0,0)) ((xy)/(x^2 + y^2 )) b) lim_((x,y)→(0,0)) ((xy + y^3 )/(x^2 + y^2 ))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{those}\:\mathrm{functions}\:\mathrm{below}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{limit} \\ $$$$\left.\mathrm{a}\right)\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}}{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.{b}\right)\:\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}\:+\:{y}^{\mathrm{3}} }{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$

Question Number 11394    Answers: 0   Comments: 0

Find equation of the hyperbolas that intersect 3x^2 −4y^2 =5xy and 3y^2 −4x^2 =2x+5.

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolas}\:\mathrm{that}\: \\ $$$$\mathrm{intersect}\:\mathrm{3x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} =\mathrm{5xy}\:\mathrm{and}\: \\ $$$$\mathrm{3y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}. \\ $$

Question Number 11393    Answers: 0   Comments: 0

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