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Question Number 211793    Answers: 0   Comments: 0

Question Number 211796    Answers: 1   Comments: 0

Question Number 211795    Answers: 0   Comments: 0

Question Number 211798    Answers: 1   Comments: 0

Question Number 211797    Answers: 4   Comments: 0

Question Number 211778    Answers: 1   Comments: 1

Show that: ∫_0 ^( (𝛑/4)) sin^4 x 2x dx = ((3Ο€ βˆ’4)/(192))

$$\:\:\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\boldsymbol{\mathrm{sin}}^{\mathrm{4}} \boldsymbol{\mathrm{x}}\:\mathrm{2}\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}\:=\:\frac{\mathrm{3}\pi\:βˆ’\mathrm{4}}{\mathrm{192}} \\ $$

Question Number 211761    Answers: 2   Comments: 0

If x = ((4a^2 b)/(4b^2 + 1)) where b > (1/2) then (((√(a^2 + x)) + (√(a^2 βˆ’ x)))/( (√(a^2 + x)) βˆ’ (√(a^2 βˆ’ x)))) = ?

$$\mathrm{If}\:{x}\:=\:\frac{\mathrm{4}{a}^{\mathrm{2}} {b}}{\mathrm{4}{b}^{\mathrm{2}} \:+\:\mathrm{1}}\:\mathrm{where}\:{b}\:>\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{then} \\ $$$$\frac{\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:+\:\sqrt{{a}^{\mathrm{2}} \:βˆ’\:{x}}}{\:\sqrt{{a}^{\mathrm{2}} \:+\:{x}}\:βˆ’\:\sqrt{{a}^{\mathrm{2}} \:βˆ’\:{x}}}\:=\:? \\ $$

Question Number 211759    Answers: 4   Comments: 1

lim_(xβ†’0) ((e^(sin x) βˆ’e^x )/(sin xβˆ’x))=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:{x}} βˆ’{e}^{{x}} }{\mathrm{sin}\:{x}βˆ’{x}}=? \\ $$

Question Number 211753    Answers: 1   Comments: 0

find all (n,m) such that ((n^2 βˆ’m)/(m^2 βˆ’n)) ∈ Z

$${find}\:{all}\:\left({n},{m}\right)\:{such}\:{that}\:\frac{{n}^{\mathrm{2}} βˆ’{m}}{{m}^{\mathrm{2}} βˆ’{n}}\:\in\:\mathbb{Z} \\ $$

Question Number 211750    Answers: 1   Comments: 0

lim_(xβ†’βˆž) (((a^(1/x) +b^(1/x) )/2))^x ;(a,b)∈R_+ ^βˆ—

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{a}^{\mathrm{1}/{x}} +{b}^{\mathrm{1}/{x}} }{\mathrm{2}}\right)^{{x}} ;\left({a},{b}\right)\in\mathbb{R}_{+} ^{\ast} \\ $$

Question Number 211749    Answers: 3   Comments: 0

volume bounded by the curve z = (√(3x^2 +3y^2 )) and x^2 +y^2 +z^2 = 6^2

$${volume}\:{bounded}\:{by}\:{the}\:{curve} \\ $$$$\:{z}\:=\:\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} }\:\:\:{and}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\:\mathrm{6}^{\mathrm{2}} \\ $$

Question Number 211745    Answers: 1   Comments: 1

lim_(xβ†’5) (10^2 +5xβˆ’20)

$$\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\mathrm{10}^{\mathrm{2}} +\mathrm{5}{x}βˆ’\mathrm{20}\right) \\ $$

Question Number 211738    Answers: 0   Comments: 1

∫(1/(x^5 +1 ))dx.

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{5}} +\mathrm{1}\:}\boldsymbol{{dx}}. \\ $$$$ \\ $$

Question Number 211734    Answers: 1   Comments: 0

Question Number 211732    Answers: 2   Comments: 0

Question Number 211730    Answers: 0   Comments: 0

Question Number 211727    Answers: 1   Comments: 0

Question Number 211726    Answers: 0   Comments: 0

Question Number 211722    Answers: 1   Comments: 0

a, b ∈ N a βˆ™ b = 144 how many different numbers can a and b be here?

$$\mathrm{a},\:\mathrm{b}\:\in\:\mathbb{N} \\ $$$$\mathrm{a}\:\centerdot\:\mathrm{b}\:=\:\mathrm{144} \\ $$$$ \\ $$how many different numbers can a and b be here?

Question Number 211720    Answers: 2   Comments: 0

if ((8^x βˆ’2^x )/(6^x βˆ’3^x )) = 2 find x

$$\:\:\:\:\:\boldsymbol{{if}}\:\:\frac{\mathrm{8}^{\boldsymbol{{x}}} βˆ’\mathrm{2}^{\boldsymbol{{x}}} }{\mathrm{6}^{\boldsymbol{{x}}} βˆ’\mathrm{3}^{\boldsymbol{{x}}} }\:\:\:=\:\mathrm{2}\:\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$

Question Number 211719    Answers: 0   Comments: 1

Question Number 211716    Answers: 1   Comments: 0

lim_(xβ†’βˆž) (1+(1/(1Γ—2))+(1/(1Γ—2Γ—3))+βˆ™βˆ™βˆ™+(1/(1Γ—2Γ—3Γ—βˆ™βˆ™βˆ™Γ—x)))=?

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

Question Number 211717    Answers: 1   Comments: 0

lim_(xβ†’0) (((1+x^2 )^(1/3) βˆ’1)/(e^x^2 βˆ’1))=?

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

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 βˆ’x^3 + x^2 + 3xβˆ’6 price range: E(f) = ?

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

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