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AllQuestion and Answers: Page 1245

Question Number 90402 Answers: 1 Comments: 0

Question Number 90432 Answers: 1 Comments: 1

lim_(x→−∞) x[(√(x^2 +1))−x ] =?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}\left[\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}\:\right]\:=? \\ $$

Question Number 90394 Answers: 1 Comments: 2

(3x^2 +9xy+5y^2 )dx = (6x^2 +4xy)dy

$$\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{9xy}+\mathrm{5y}^{\mathrm{2}} \right)\mathrm{dx}\:=\:\left(\mathrm{6x}^{\mathrm{2}} +\mathrm{4xy}\right)\mathrm{dy} \\ $$

Question Number 90383 Answers: 0 Comments: 1

find the values of a and b such that the following function differentiable at x=1 f(x) = { ((x^2 , x≤1)),((2ax+b , x>1)) :}

$$\mathrm{find}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{function}\:\mathrm{differentiable}\:\mathrm{at}\: \\ $$$$\mathrm{x}=\mathrm{1}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} ,\:\mathrm{x}\leqslant\mathrm{1}}\\{\mathrm{2ax}+\mathrm{b}\:,\:\mathrm{x}>\mathrm{1}}\end{cases} \\ $$

Question Number 90379 Answers: 0 Comments: 2

Question Number 90440 Answers: 0 Comments: 3

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 =...?

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

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