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Question Number 213797 Answers: 1 Comments: 0

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⋗

$$\:\:\:\cancel{\underbrace{\gtrdot}}\: \\ $$

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lim_(x→0) ((10^x −1)/x^(10) )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{10}^{\mathrm{x}} −\mathrm{1}}{\mathrm{x}^{\mathrm{10}} } \\ $$

Question Number 206294 Answers: 2 Comments: 2

Solve the system (a+b)^(−1) +c^(−1) =2^(−1) (c+b)^(−1) +a^(−1) =3^(−1) (a+c)^(−1) +b^(−1) =4^(−1)

$${Solve}\:{the}\:{system} \\ $$$$\left({a}+{b}\right)^{−\mathrm{1}} +{c}^{−\mathrm{1}} =\mathrm{2}^{−\mathrm{1}} \\ $$$$\left({c}+{b}\right)^{−\mathrm{1}} +{a}^{−\mathrm{1}} =\mathrm{3}^{−\mathrm{1}} \\ $$$$\left({a}+{c}\right)^{−\mathrm{1}} +{b}^{−\mathrm{1}} =\mathrm{4}^{−\mathrm{1}} \\ $$

Question Number 206212 Answers: 2 Comments: 4

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Value of x?

$$\mathrm{Value}\:\mathrm{of}\:\boldsymbol{\mathrm{x}}? \\ $$

Question Number 200249 Answers: 1 Comments: 1

Solve: find the distance of the point P(3,4) from the line y=−2x+3

$$\boldsymbol{{Solve}}:\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{distance}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\boldsymbol{{P}}\left(\mathrm{3},\mathrm{4}\right)\:\boldsymbol{{from}}\:\boldsymbol{{the}}\:\boldsymbol{{line}}\:\boldsymbol{{y}}=−\mathrm{2}\boldsymbol{{x}}+\mathrm{3} \\ $$

Question Number 198749 Answers: 0 Comments: 0

Find area bounded by curve below cx^3 +c^2 +y(y+1)^2 =x^2 y+cx(3y+1)

$${Find}\:{area}\:{bounded}\:{by}\:{curve}\:{below} \\ $$$${cx}^{\mathrm{3}} +{c}^{\mathrm{2}} +{y}\left({y}+\mathrm{1}\right)^{\mathrm{2}} ={x}^{\mathrm{2}} {y}+{cx}\left(\mathrm{3}{y}+\mathrm{1}\right) \\ $$

Question Number 197950 Answers: 0 Comments: 0

Let x,y,z>0 , x+y+z=3 Prove That : (1/( (√(x^2 +2x))))+(1/( (√(z^2 +2z))))+(√3)((1/(y+2))−(y/9))+((((√x)+(√y)+(√z)+24))^(1/3) /( (√3)))≥((17)/(3(√3)))

$${Let}\:{x},{y},{z}>\mathrm{0}\:,\:{x}+{y}+{z}=\mathrm{3}\:{Prove}\:{That}\:: \\ $$$$\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}}}+\frac{\mathrm{1}}{\:\sqrt{{z}^{\mathrm{2}} +\mathrm{2}{z}}}+\sqrt{\mathrm{3}}\left(\frac{\mathrm{1}}{{y}+\mathrm{2}}−\frac{{y}}{\mathrm{9}}\right)+\frac{\sqrt[{\mathrm{3}}]{\sqrt{{x}}+\sqrt{{y}}+\sqrt{{z}}+\mathrm{24}}}{\:\sqrt{\mathrm{3}}}\geqslant\frac{\mathrm{17}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$

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Question Number 196320 Answers: 1 Comments: 0

If a regular n−polygon can be divided into n identical equilateral triangles then n=6

$$\:\:{If}\:\:{a}\:\:{regular}\:{n}−{polygon}\:{can} \\ $$$$\:{be}\:{divided}\:{into}\:\:{n}\:\:{identical}\:\: \\ $$$${equilateral}\:{triangles}\:{then}\:\:{n}=\mathrm{6} \\ $$

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Question Number 195790 Answers: 1 Comments: 2

a,b,c are positive real numbers and abc =1 prove that (a−1+(1/b))(b−1+(1/c))(c−1+(1/a))≤1

$${a},{b},{c}\:{are}\:{positive}\:{real}\:{numbers}\:{and}\:{abc}\:=\mathrm{1} \\ $$$${prove}\:{that} \\ $$$$\left({a}−\mathrm{1}+\frac{\mathrm{1}}{{b}}\right)\left({b}−\mathrm{1}+\frac{\mathrm{1}}{{c}}\right)\left({c}−\mathrm{1}+\frac{\mathrm{1}}{{a}}\right)\leqslant\mathrm{1} \\ $$

Question Number 195611 Answers: 1 Comments: 0

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Given three Real numbers (x,y,z),such that x^2 +y^2 +z^2 =1 maximize x^4 +y^4 −2z^4 −3(√2)xyz

$$\mathrm{Given}\:\mathrm{three}\:\mathrm{Real}\:\mathrm{numbers}\:\left({x},{y},{z}\right),{such}\:{that} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{1} \\ $$$${maximize} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} −\mathrm{2}{z}^{\mathrm{4}} −\mathrm{3}\sqrt{\mathrm{2}}{xyz} \\ $$

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