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AllQuestion and Answers: Page 1228

Question Number 85130 Answers: 2 Comments: 0

given f(x)= ((√2)+1)sin x +((√2)−1)cos x find masimum value of function [f(x)]^2

$$\mathrm{given}\:\mathrm{f}\left(\mathrm{x}\right)=\:\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\mathrm{sin}\:\mathrm{x}\:+\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\mathrm{cos}\:\mathrm{x} \\ $$$$\mathrm{find}\:\mathrm{masimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\left[\mathrm{f}\left(\mathrm{x}\right)\right]^{\mathrm{2}} \\ $$

Question Number 85129 Answers: 0 Comments: 2

lim_(x→e) [∫_0 ^e ((1/x))dx] =?

$$\underset{{x}\rightarrow{e}} {\mathrm{lim}}\:\left[\underset{\mathrm{0}} {\overset{{e}} {\int}}\left(\frac{\mathrm{1}}{{x}}\right){dx}\right]\:=? \\ $$

Question Number 85127 Answers: 1 Comments: 4

evaluate: lim_(x→0) (√x) ln(sin x)

$$\mathrm{evaluate}: \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{{x}}\:\mathrm{ln}\left(\mathrm{sin}\:{x}\right) \\ $$$$ \\ $$

Question Number 85116 Answers: 0 Comments: 1

Reduce the equations to Clairaut′s form and find the general solution : x^2 p^2 +yp(2x+y)+y^2 =0 (put y=u and xy=v)

$$\:\mathrm{Reduce}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{to}\:\mathrm{Clairaut}'\mathrm{s}\:\mathrm{form} \\ $$$$\:\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:: \\ $$$$\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{p}}^{\mathrm{2}} +\boldsymbol{\mathrm{yp}}\left(\mathrm{2}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)+\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{0}\:\:\:\:\:\:\left({put}\:\boldsymbol{{y}}=\boldsymbol{{u}}\:{and}\:\boldsymbol{{xy}}=\boldsymbol{{v}}\right) \\ $$$$\: \\ $$

Question Number 85111 Answers: 1 Comments: 4

Solve the differential equation: ★.(1+x+xy^2 )dy+(y+y^3 )dx

$$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\bigstar.\left(\mathrm{1}+\mathrm{x}+\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dy}+\left(\mathrm{y}+\mathrm{y}^{\mathrm{3}} \right)\mathrm{dx} \\ $$$$\: \\ $$

Question Number 85105 Answers: 1 Comments: 0

Question Number 85104 Answers: 1 Comments: 2

Given { ((x^2 −2xy−3x = −1)),((4y^2 −2xy+6y = −1)) :} find 2y − x

$$\mathrm{Given}\: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2xy}−\mathrm{3x}\:=\:−\mathrm{1}}\\{\mathrm{4y}^{\mathrm{2}} −\mathrm{2xy}+\mathrm{6y}\:=\:−\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{2y}\:−\:\mathrm{x} \\ $$

Question Number 85103 Answers: 0 Comments: 0

Question Number 85097 Answers: 1 Comments: 0

∫_(−π) ^π x^(2020) (sin x+cos x) dx = 8 find ∫_(−π) ^π x^(2020) cos x dx = ?

$$\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{8} \\ $$$$\mathrm{find}\:\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:=\:? \\ $$

Question Number 85091 Answers: 0 Comments: 1

Question Number 85088 Answers: 0 Comments: 1

Question Number 85083 Answers: 0 Comments: 1

a^3 −b^3 =...?

$${a}^{\mathrm{3}} −{b}^{\mathrm{3}} =...? \\ $$

Question Number 85074 Answers: 1 Comments: 1

Question Number 85073 Answers: 0 Comments: 1

Prove by mathematical induction that 2002^(n+2) +2003^(2n+1) is divisible by 4005

$${Prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$$\mathrm{2002}^{{n}+\mathrm{2}} +\mathrm{2003}^{\mathrm{2}{n}+\mathrm{1}} \:\:\:\:{is}\:{divisible}\:{by}\:\mathrm{4005} \\ $$

Question Number 85068 Answers: 0 Comments: 3

Question Number 85061 Answers: 1 Comments: 3

lim_(x→0) ((x tan2x−2x tan(x))/((1−cos(2x))^2 ))

$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{x}\:{tan}\mathrm{2}{x}−\mathrm{2}{x}\:{tan}\left({x}\right)}{\left(\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)\right)^{\mathrm{2}} } \\ $$

Question Number 85059 Answers: 1 Comments: 0

Question Number 85057 Answers: 0 Comments: 1

find lim_(x→0) ln (sin xcos (1/x)+1) if it exits.

$${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}ln}\:\left(\mathrm{sin}\:{x}\mathrm{cos}\:\frac{\mathrm{1}}{{x}}+\mathrm{1}\right)\:{if}\:{it}\:{exits}. \\ $$

Question Number 85050 Answers: 1 Comments: 0

(x−4y+3)dx = (x−5y+4)dy

$$\left(\mathrm{x}−\mathrm{4y}+\mathrm{3}\right)\mathrm{dx}\:=\:\left(\mathrm{x}−\mathrm{5y}+\mathrm{4}\right)\mathrm{dy} \\ $$

Question Number 85041 Answers: 0 Comments: 0

Question Number 85036 Answers: 0 Comments: 1

If A= [((x x x )),((4_(2 ) −2_3 1_4 )) ]findX if p(A)=3

$${If}\:{A}=\begin{bmatrix}{{x}\:\:\:\:{x}\:\:\:{x}\:\:}\\{\underset{\mathrm{2}\:\:} {\mathrm{4}}\:−\underset{\mathrm{3}} {\mathrm{2}}\:\:\:\underset{\mathrm{4}} {\mathrm{1}}}\end{bmatrix}{findX}\:{if}\:{p}\left({A}\right)=\mathrm{3} \\ $$$$ \\ $$$$ \\ $$

Question Number 85021 Answers: 0 Comments: 0

lim_(x→0) ((tan^4 (x) cot(ln^3 (x+1))ln(sin^3 (x)cos^2 (x)+1))/(sin((√(x^2 +2)) −(√2))ln(x^2 +1)))

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

Question Number 85020 Answers: 0 Comments: 4

solve integration ∫_1 ^2 x d⌊x^2 ⌋

$${solve}\:{integration} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}} {x}\:{d}\lfloor{x}^{\mathrm{2}} \rfloor \\ $$

Question Number 85009 Answers: 1 Comments: 1

calculate ∫_0 ^∞ (x^n /(sh(x)))dx with n integr natural

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{x}^{{n}} }{{sh}\left({x}\right)}{dx}\:{with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 85003 Answers: 1 Comments: 7

x≤[x]<x+1 is that right if (x) was negative

$${x}\leqslant\left[{x}\right]<{x}+\mathrm{1} \\ $$$${is}\:{that}\:{right}\:{if}\:\left({x}\right)\:{was}\:{negative} \\ $$

Question Number 84998 Answers: 2 Comments: 0

what is coefficient of x^(29) in expression (1+x^5 +x^7 +x^9 )^(29)

$$\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{29}} \\ $$$$\mathrm{in}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{7}} +\mathrm{x}^{\mathrm{9}} \right)^{\mathrm{29}} \\ $$

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