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Question Number 211716 Answers: 1 Comments: 0

lim_(x→∞) (1+(1/(1×2))+(1/(1×2×3))+∙∙∙+(1/(1×2×3×∙∙∙×x)))=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}}+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}×\mathrm{3}×\centerdot\centerdot\centerdot×{x}}\right)=? \\ $$

Question Number 211717 Answers: 1 Comments: 0

lim_(x→0) (((1+x^2 )^(1/3) −1)/(e^x^2 −1))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{li}{m}}\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{1}}{{e}^{{x}^{\mathrm{2}} } −\mathrm{1}}=? \\ $$

Question Number 211706 Answers: 1 Comments: 0

if x^(log27) + 9^(logx) =36 find x

$$\:\:\:\:\:\boldsymbol{{if}}\:\:\boldsymbol{{x}}^{\boldsymbol{{log}}\mathrm{27}} +\:\:\:\mathrm{9}^{\boldsymbol{{logx}}} =\mathrm{36}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$

Question Number 211703 Answers: 0 Comments: 2

Calculate the quadruple integralas follows: I=∫_0 ^1 ∫_0 ^x ∫_0 ^y ∫_0 ^z ((sin(x^2 +y^2 +z^2 +w^2 ))/(1+w^2 +z^2 ))dw dz dy dx

$$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{w}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{{w}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} }\boldsymbol{{dw}}\:\boldsymbol{{dz}}\:\boldsymbol{\mathrm{dy}}\:\boldsymbol{{dx}} \\ $$$$ \\ $$

Question Number 211700 Answers: 0 Comments: 1

f(x) = x^4 −x^3 + x^2 + 3x−6 price range: E(f) = ?

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{3x}−\mathrm{6} \\ $$$$\mathrm{price}\:\mathrm{range}:\:\mathrm{E}\left(\mathrm{f}\right)\:=\:? \\ $$

Question Number 211696 Answers: 1 Comments: 0

∫^( 1) _0 (( 1)/(( 2 +2x + x^2 )^3 )) dx= ? _( ^(Improper integral ) ) −−−−−−−−−

$$ \\ $$$$\:\:\:\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{\:\:\mathrm{1}}{\left(\:\mathrm{2}\:+\mathrm{2}{x}\:+\:{x}^{\mathrm{2}} \:\right)^{\mathrm{3}} }\:{dx}=\:? \\ $$$$\:\:\:\:\:\:\underbrace{\underset{\:\:\:\:\overset{\mathrm{Improper}\:\mathrm{integral}\:} {\:}\:\:\:\:\:} {\:}} \\ $$$$\:\:\:\:\:\:\:\:−−−−−−−−− \\ $$

Question Number 211694 Answers: 0 Comments: 4

Question Number 211691 Answers: 1 Comments: 0

Question Number 211680 Answers: 1 Comments: 1

x, y are positive integer such that, x^3 +y^3 +xy=911. (x,y)=?

$$\:{x},\:{y}\:{are}\:{positive}\:{integer}\:{such}\: \\ $$$$\:\:{that},\:{x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{xy}=\mathrm{911}.\:\left({x},{y}\right)=? \\ $$

Question Number 211679 Answers: 1 Comments: 1

Inverse root formula: x=((2c)/(−b±(√(b^2 −4ac)))) (1)The“ antiroot formula” is derivedr fom the abovementionedt antiroo formula.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Inverse}\:\mathrm{root}\:\mathrm{formula}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}=\frac{\mathrm{2}\boldsymbol{{c}}}{−\boldsymbol{{b}}\pm\sqrt{\boldsymbol{{b}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{ac}}}} \\ $$$$\left(\mathrm{1}\right)\mathrm{The}``\:\mathrm{antiroot}\:\mathrm{formula}''\:\mathrm{is}\:\mathrm{derivedr} \\ $$$$\mathrm{fom}\:\mathrm{the}\:\mathrm{abovementionedt} \\ $$$$\mathrm{antiroo}\:\mathrm{formula}. \\ $$

Question Number 213343 Answers: 1 Comments: 0

Question Number 213342 Answers: 0 Comments: 1

Question Number 213341 Answers: 2 Comments: 3

Question Number 213340 Answers: 0 Comments: 3

Question Number 213369 Answers: 2 Comments: 0

Old question 203835 ∫_0 ^(√2) ((√(6−(√(25x^4 −50x^2 +36))))/( (√5)))dx=?

$$\mathrm{Old}\:\mathrm{question}\:\mathrm{203835} \\ $$$$\underset{\mathrm{0}} {\overset{\sqrt{\mathrm{2}}} {\int}}\frac{\sqrt{\mathrm{6}−\sqrt{\mathrm{25}{x}^{\mathrm{4}} −\mathrm{50}{x}^{\mathrm{2}} +\mathrm{36}}}}{\:\sqrt{\mathrm{5}}}{dx}=? \\ $$

Question Number 211675 Answers: 2 Comments: 1

x^2 =2^x Find more than three solutions

$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{2}} =\mathrm{2}^{\boldsymbol{{x}}} \\ $$$$\:\mathrm{Find}\:\mathrm{more}\:\mathrm{than}\:\mathrm{three}\:\mathrm{solutions} \\ $$$$ \\ $$

Question Number 211673 Answers: 1 Comments: 0

Resoudre ^x (√(x/(x−1))) =(x−1)^((x−2)) .

$$\:\:\:\boldsymbol{{Resoudre}} \\ $$$$\:\:^{\boldsymbol{\mathrm{x}}} \sqrt{\frac{\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}−\mathrm{1}}}\:\:\:=\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)^{\left(\boldsymbol{\mathrm{x}}−\mathrm{2}\right)} . \\ $$

Question Number 211672 Answers: 0 Comments: 2

In a triangle the bisector of the side c is perpendicular to side b. Prove that 2tanC + tanA = 0.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:{c}\:\mathrm{is} \\ $$$$\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{side}\:{b}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{2tanC}\:+\:\mathrm{tanA}\:=\:\mathrm{0}. \\ $$

Question Number 211659 Answers: 2 Comments: 1

Question Number 211658 Answers: 2 Comments: 0

(√(19−8(√3))) x^2 −ax+ b =0 a b a + b .

$$\:\: \sqrt{\mathrm{19}−\mathrm{8}\sqrt{\mathrm{3}}}\: \\ $$$$ \mathrm{x}^{\mathrm{2}} −{a}\mathrm{x}+\:{b}\:=\mathrm{0}\: {a}\: {b}\: \\ $$$$ \\ $$$$ {a}\:+\:{b}\:.\: \\ $$

Question Number 211657 Answers: 1 Comments: 0

sin(9x) = sin(5x) + sin(3x) find: x = ?

$$\mathrm{sin}\left(\mathrm{9x}\right)\:=\:\mathrm{sin}\left(\mathrm{5x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right) \\ $$$$\mathrm{find}:\:\:\mathrm{x}\:=\:? \\ $$

Question Number 211651 Answers: 1 Comments: 0

In triangle ABC, ∠C = 60°. If the length of opposite sides of ∠A, ∠B and ∠C are a, b and c respectively then prove that (1/(a + c)) + (1/(b + c)) = (3/(a + b + c)) .

$$\mathrm{In}\:\mathrm{triangle}\:\mathrm{ABC},\:\angle\mathrm{C}\:=\:\mathrm{60}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{opposite}\:\mathrm{sides}\:\mathrm{of}\:\angle\mathrm{A},\:\angle\mathrm{B}\:\mathrm{and}\:\angle\mathrm{C}\:\mathrm{are} \\ $$$${a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{respectively}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}\:+\:{c}}\:+\:\frac{\mathrm{1}}{{b}\:+\:{c}}\:=\:\frac{\mathrm{3}}{{a}\:+\:{b}\:+\:{c}}\:. \\ $$

Question Number 211643 Answers: 1 Comments: 0

Let A={x ∈ R∣x^2 <4}and B={y ∈ Q∣y>−3}find A∩B

$$\mathrm{Let}\:\boldsymbol{{A}}=\left\{\boldsymbol{{x}}\:\in\:\mathbb{R}\mid\boldsymbol{{x}}^{\mathrm{2}} <\mathrm{4}\right\}\mathrm{and} \\ $$$$\boldsymbol{{B}}=\left\{\boldsymbol{{y}}\:\in\:\mathbb{Q}\mid\boldsymbol{{y}}>−\mathrm{3}\right\}\mathrm{find}\:\boldsymbol{{A}}\cap\boldsymbol{{B}} \\ $$

Question Number 211637 Answers: 1 Comments: 0

f(x) = sin x − e^x + 1. Prove that f(x) has only 2 zeros in −π≤x≤0.

$${f}\left({x}\right)\:=\:\mathrm{sin}\:{x}\:−\:\mathrm{e}^{{x}} \:+\:\mathrm{1}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{has}\:\mathrm{only}\:\mathrm{2}\:\mathrm{zeros}\:\mathrm{in}\:−\pi\leqslant{x}\leqslant\mathrm{0}. \\ $$

Question Number 211636 Answers: 1 Comments: 0

Question Number 211635 Answers: 1 Comments: 0

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