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Question Number 187607    Answers: 0   Comments: 1

Help! :( Should i partially differentiate the numerator and denominator? lim_((x, y)→(0,1)) [((x^e + ln((1/y)))/(x^e − ln((1/y))))]

$$\: \\ $$$$\:\boldsymbol{\mathrm{Help}}!\:\::\left(\right. \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Should}}\:\:\boldsymbol{\mathrm{i}}\:\:\boldsymbol{\mathrm{partially}}\:\:\boldsymbol{\mathrm{differentiate}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{numerator}}\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{denominator}}? \\ $$$$\: \\ $$$$\:\underset{\left(\boldsymbol{{x}},\:\boldsymbol{\mathrm{y}}\right)\rightarrow\left(\mathrm{0},\mathrm{1}\right)} {\boldsymbol{\mathrm{lim}}}\left[\frac{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:\:+\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:−\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}\right] \\ $$

Question Number 187605    Answers: 0   Comments: 0

what is the name of the shape whose graph is: (a) f(x,y)=(√(x^2 +y^2 )) (b) f(x,y)=x^2 +y^2 (c) f(x,y)=(√(1−x^2 −y^2 )) (d) f(x,y)=x^2 +y^2 −2x (e) f(x,y)=xy

$$\:{what}\:{is}\:{the}\:{name}\:{of}\:{the}\:{shape}\:{whose} \\ $$$${graph}\:{is}: \\ $$$$\left({a}\right)\:{f}\left({x},{y}\right)=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$$\: \\ $$$$\:\left({b}\right)\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$$$\: \\ $$$$\:\:\left({c}\right)\:{f}\left({x},{y}\right)=\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$\:\:\:\:\left({d}\right)\:{f}\left({x},{y}\right)={x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x} \\ $$$$ \\ $$$$\:\:\:\:\left({e}\right)\:{f}\left({x},{y}\right)={xy} \\ $$

Question Number 187606    Answers: 2   Comments: 0

Use polar coordinate to find lim(x,y)→(0,0) ((x^2 −xy^2 )/(x^2 +y^2 ))

$$\:{Use}\:{polar}\:{coordinate}\:{to}\:{find}\: \\ $$$${lim}\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)\:\frac{{x}^{\mathrm{2}} −{xy}^{\mathrm{2}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$

Question Number 187602    Answers: 1   Comments: 0

∫_(1/4) ^(1/2) ((sin^(−1) ((√x))−cos^(−1) ((√x)))/(sin^(−1) ((√x))+cos^(−1) ((√x)))) dx=?

$$\:\:\:\underset{\mathrm{1}/\mathrm{4}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{{x}}\right)−\mathrm{cos}^{−\mathrm{1}} \left(\sqrt{{x}}\right)}{\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{{x}}\right)+\mathrm{cos}^{−\mathrm{1}} \left(\sqrt{{x}}\right)}\:{dx}=? \\ $$

Question Number 187598    Answers: 2   Comments: 0

lim_(x→0^+ ) (6/x)−(√(((36)/x^2 )+(4/x)+9)) =?

$$\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\mathrm{6}}{{x}}−\sqrt{\frac{\mathrm{36}}{{x}^{\mathrm{2}} }+\frac{\mathrm{4}}{{x}}+\mathrm{9}}\:=? \\ $$

Question Number 187595    Answers: 1   Comments: 1

Question Number 187589    Answers: 3   Comments: 1

Question Number 187587    Answers: 2   Comments: 1

Question Number 187585    Answers: 1   Comments: 1

Question Number 187581    Answers: 0   Comments: 0

Question Number 187560    Answers: 1   Comments: 0

Question Number 187559    Answers: 1   Comments: 0

Question Number 187557    Answers: 3   Comments: 0

Question Number 187556    Answers: 0   Comments: 1

Question Number 187549    Answers: 1   Comments: 0

Question Number 187548    Answers: 2   Comments: 0

Question Number 187546    Answers: 2   Comments: 0

Question Number 187541    Answers: 0   Comments: 1

Quel est la condition necessaire et sufisante pour que les medianes des triangles ABC et CDE soient alignes avec le point c

$${Quel}\:{est}\:{la}\:{condition}\:{necessaire} \\ $$$${et}\:{sufisante}\:{pour}\:{que}\:{les}\:{medianes} \\ $$$${des}\:{triangles}\:{ABC}\:{et}\:\:{CDE}\:{soient} \\ $$$${alignes}\:{avec}\:{le}\:{point}\:\boldsymbol{{c}} \\ $$$$ \\ $$

Question Number 187535    Answers: 1   Comments: 1

Question Number 187534    Answers: 0   Comments: 0

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Question Number 187531    Answers: 3   Comments: 0

∫_0 ^∞ x^2 e^(−x) dx=?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}{x}^{\mathrm{2}} {e}^{−{x}} {dx}=? \\ $$

Question Number 187530    Answers: 1   Comments: 0

∫(dx/( (√(a^2 +be^(cx) ))))=?

$$\int\frac{{dx}}{\:\sqrt{{a}^{\mathrm{2}} +{be}^{{cx}} }}=? \\ $$

Question Number 187529    Answers: 1   Comments: 0

∫x^2 ∙sin^(−1) (x)dx=?

$$\int{x}^{\mathrm{2}} \centerdot{sin}^{−\mathrm{1}} \left({x}\right){dx}=? \\ $$

Question Number 187528    Answers: 1   Comments: 0

∫_((9π)/2) ^((7π)/(1.5)) (dx/( (√(1−sinx))))=?

$$\underset{\frac{\mathrm{9}\pi}{\mathrm{2}}} {\overset{\frac{\mathrm{7}\pi}{\mathrm{1}.\mathrm{5}}} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}−{sinx}}}=? \\ $$

Question Number 187526    Answers: 2   Comments: 0

∫(dx/(cscx−1))=?

$$\int\frac{{dx}}{{cscx}−\mathrm{1}}=? \\ $$

Question Number 187525    Answers: 1   Comments: 0

∫_(−1) ^2 (dx/( (√(∣x−1∣))))=?

$$\underset{−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\frac{{dx}}{\:\sqrt{\mid{x}−\mathrm{1}\mid}}=? \\ $$

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