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AllQuestion and Answers: Page 1226

Question Number 90362 Answers: 0 Comments: 7

Question Number 90360 Answers: 1 Comments: 1

Question Number 90359 Answers: 0 Comments: 1

∫(1/(sin^2 (x)))

$$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \left({x}\right)} \\ $$

Question Number 90358 Answers: 0 Comments: 0

Question Number 90357 Answers: 0 Comments: 0

∫ ((x.2^x )/(√(1−x^2 ))) dx = ?

$$\int\:\frac{{x}.\mathrm{2}^{{x}} }{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\:=\:? \\ $$

Question Number 90356 Answers: 0 Comments: 0

Question Number 90350 Answers: 1 Comments: 0

n^2 x−5a^2 y^2 −n^2 y^2 +5a^2 x

$${n}^{\mathrm{2}} {x}−\mathrm{5}{a}^{\mathrm{2}} {y}^{\mathrm{2}} −{n}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{5}{a}^{\mathrm{2}} {x} \\ $$

Question Number 90347 Answers: 2 Comments: 5

Question Number 90341 Answers: 0 Comments: 0

Express x^2 +y^2 =36 interm conjugate coordinate

$${Express}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{36}\:\:{interm} \\ $$$${conjugate}\:{coordinate} \\ $$

Question Number 90331 Answers: 1 Comments: 1

Question Number 90330 Answers: 0 Comments: 1

Question Number 90327 Answers: 0 Comments: 1

Question Number 90326 Answers: 1 Comments: 1

Question Number 90321 Answers: 2 Comments: 2

∫(1/(x((1+x^5 ))^(1/3) ))dx ∫(1/(sin^2 (x)+5sin(x)+6))dx ∫((2z−5)/(4z^2 +4z+5))dz ∫sec^5 (5θ) (√(tan^3 (5θ))) dθ

$$\int\frac{\mathrm{1}}{{x}\sqrt[{\mathrm{3}}]{\mathrm{1}+{x}^{\mathrm{5}} }}{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{1}}{{sin}^{\mathrm{2}} \left({x}\right)+\mathrm{5}{sin}\left({x}\right)+\mathrm{6}}{dx} \\ $$$$ \\ $$$$\int\frac{\mathrm{2}{z}−\mathrm{5}}{\mathrm{4}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{5}}{dz} \\ $$$$ \\ $$$$\int{sec}^{\mathrm{5}} \left(\mathrm{5}\theta\right)\:\sqrt{{tan}^{\mathrm{3}} \left(\mathrm{5}\theta\right)}\:{d}\theta \\ $$$$ \\ $$$$ \\ $$

Question Number 90318 Answers: 0 Comments: 0

Please can this be resolve in partial fraction? ((sec^2 x − (2/x^2 ))/((tan x + (1/x))^2 ))

$$\mathrm{Please}\:\mathrm{can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{resolve}\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fraction}? \\ $$$$\:\:\:\:\:\:\frac{\mathrm{sec}^{\mathrm{2}} \mathrm{x}\:\:−\:\:\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }}{\left(\mathrm{tan}\:\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} } \\ $$

Question Number 90316 Answers: 1 Comments: 2

determinant ((x,7),(9,(8−x)))= determinant ((7,0,(−3)),((−5),x,(−6)),((−3),(−5),(x−9)))

$$\begin{vmatrix}{{x}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{8}−{x}}\end{vmatrix}=\begin{vmatrix}{\mathrm{7}}&{\mathrm{0}}&{−\mathrm{3}}\\{−\mathrm{5}}&{{x}}&{−\mathrm{6}}\\{−\mathrm{3}}&{−\mathrm{5}}&{{x}−\mathrm{9}}\end{vmatrix} \\ $$$$ \\ $$

Question Number 90307 Answers: 1 Comments: 0

Solve the differential equation. (x^2 D^2 −2)y = x^2 + (1/x).

$$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}. \\ $$$$\:\:\:\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{D}}^{\mathrm{2}} −\mathrm{2}\right)\boldsymbol{\mathrm{y}}\:=\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:+\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}. \\ $$

Question Number 90306 Answers: 2 Comments: 2

lim_(λ→0) ∫_λ ^(2λ) (e^(−x) /x)dx

$$\underset{\lambda\rightarrow\mathrm{0}} {\mathrm{lim}}\int_{\lambda} ^{\mathrm{2}\lambda} \:\frac{{e}^{−{x}} }{{x}}{dx} \\ $$

Question Number 90308 Answers: 1 Comments: 1

∫_0 ^1 (1/x)ln(((1+x)/(1−x)))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{{x}}{ln}\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right){dx} \\ $$

Question Number 90301 Answers: 0 Comments: 1

Help me z(x,y)=y.e^(x/y) . z′_x =...? and z′_y =...?

$$\mathrm{Help}\:\mathrm{me} \\ $$$$ \\ $$$$\mathrm{z}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{y}.\mathrm{e}^{\frac{\mathrm{x}}{\mathrm{y}}} . \\ $$$$\mathrm{z}'_{\mathrm{x}} =...?\:\mathrm{and}\:\mathrm{z}'_{\mathrm{y}} =...? \\ $$

Question Number 90299 Answers: 0 Comments: 0

help me z(x,y)=xy.ln xy z_x ^′ =...? and z′_y =...?

$$\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$$$\mathrm{z}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{xy}.\mathrm{ln}\:\mathrm{xy} \\ $$$$\mathrm{z}_{\mathrm{x}} ^{'} =...?\:\:\:\mathrm{and}\:\:\mathrm{z}'_{\mathrm{y}} =...? \\ $$

Question Number 90292 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((1−e^(zx^2 ) )/x^2 )dx with z from C and Re(z)<0

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{e}^{{zx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}\:{with}\:{z}\:{from}\:{C}\:{and}\:{Re}\left({z}\right)<\mathrm{0} \\ $$

Question Number 90291 Answers: 0 Comments: 2

calculste ∫_0 ^∞ ((1−e^(zx) )/x)dx with z from C and Re(z)>0

$${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{e}^{{zx}} }{{x}}{dx}\:\:{with}\:{z}\:{from}\:{C}\:{and}\:{Re}\left({z}\right)>\mathrm{0} \\ $$

Question Number 90287 Answers: 1 Comments: 0

f(x) = { ((x^2 −2x+6 , x≥1)),((x^4 +2x^3 +2 ,x<1)) :} show that there is a number c ∈ (−2,3) such that f(c) = 4

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{6}\:,\:\mathrm{x}\geqslant\mathrm{1}}\\{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{2}\:,\mathrm{x}<\mathrm{1}}\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{c}\:\in\:\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{c}\right)\:=\:\mathrm{4} \\ $$

Question Number 90282 Answers: 0 Comments: 1

(1/(2α+β))+(1/(α+2β))

$$\frac{\mathrm{1}}{\mathrm{2}\alpha+\beta}+\frac{\mathrm{1}}{\alpha+\mathrm{2}\beta} \\ $$

Question Number 90281 Answers: 0 Comments: 2

lim_(x→1) ((1−(√x))/((cos^(−1) (x))^2 )) = ?

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

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