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AllQuestion and Answers: Page 502

Question Number 167120    Answers: 3   Comments: 0

Question Number 167086    Answers: 0   Comments: 1

Question Number 167085    Answers: 0   Comments: 1

lim_(x→∞) ((√(x^2 +3x))−(√(x^2 +x)))^x =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−\sqrt{{x}^{\mathrm{2}} +{x}}\right)^{{x}} =? \\ $$

Question Number 167082    Answers: 1   Comments: 1

Question Number 167078    Answers: 0   Comments: 2

Question Number 167077    Answers: 0   Comments: 0

Question Number 167073    Answers: 1   Comments: 0

Let the triangle A(−3; 2), B(8; 4), C(4; −6), solve:_ ^ (a)^ find the perimeter; (b)^ find the area; (c)^ find the base; (d)^ find the height; (e)^ classify it

$$\:\boldsymbol{\mathrm{Let}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{triangle}}\:\:\boldsymbol{\mathrm{A}}\left(−\mathrm{3};\:\mathrm{2}\right),\:\:\boldsymbol{\mathrm{B}}\left(\mathrm{8};\:\mathrm{4}\right),\:\:\boldsymbol{\mathrm{C}}\left(\mathrm{4};\:−\mathrm{6}\right),\:\:\boldsymbol{\mathrm{solve}}\underset{\:} {\overset{\:} {:}} \\ $$$$\:\left(\boldsymbol{\mathrm{a}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{perimeter}}; \\ $$$$\:\left(\boldsymbol{\mathrm{b}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{area}}; \\ $$$$\:\left(\boldsymbol{\mathrm{c}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{base}}; \\ $$$$\:\left(\boldsymbol{\mathrm{d}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{height}}; \\ $$$$\:\left(\boldsymbol{\mathrm{e}}\overset{\:} {\right)}\:\boldsymbol{\mathrm{classify}}\:\:\boldsymbol{\mathrm{it}} \\ $$

Question Number 167067    Answers: 0   Comments: 0

∫ln∣sinx∣dx

$$\int{ln}\mid{sinx}\mid{dx} \\ $$

Question Number 167066    Answers: 0   Comments: 1

Question Number 167058    Answers: 1   Comments: 0

Question Number 167056    Answers: 1   Comments: 0

help me! lim_(x→∞) cosec^(−1) (2)(√(x(√(2(√x)))))

$$\mathrm{help}\:\mathrm{me}!\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}cosec}^{−\mathrm{1}} \left(\mathrm{2}\right)\sqrt{{x}\sqrt{\mathrm{2}\sqrt{{x}}}} \\ $$

Question Number 167048    Answers: 1   Comments: 0

prove that Φ= ∫_0 ^( 1) x.ψ (2+x )= 2 −(1/2)ln(8π) −−−

$$ \\ $$$$\:\:\:\:\:{prove}\:{that} \\ $$$$ \\ $$$$\Phi=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}.\psi\:\left(\mathrm{2}+{x}\:\right)=\:\mathrm{2}\:−\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{8}\pi\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:−−− \\ $$

Question Number 167054    Answers: 1   Comments: 0

f(x)= { ((e^(−x^2 ) 0<x<∞)),((e^(−x^4 ) −∞<x<0 )) :} Find geometric mean of f(x)

$${f}\left({x}\right)=\begin{cases}{{e}^{−{x}^{\mathrm{2}} } \:\:\mathrm{0}<{x}<\infty}\\{{e}^{−{x}^{\mathrm{4}} } \:−\infty<{x}<\mathrm{0}\:\:\:\:}\end{cases} \\ $$$$ \\ $$$$\:{Find}\:{geometric}\:{mean}\:{of}\:{f}\left({x}\right) \\ $$

Question Number 167043    Answers: 1   Comments: 0

Question Number 167040    Answers: 0   Comments: 1

∫_0 ^( (π/2)) (1/(1+sin^6 x)) dx=?

$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}}\:\mathrm{dx}=? \\ $$

Question Number 167038    Answers: 0   Comments: 1

Find all values of a and b such that y=0,5x^2 +(a+b)x+ab is always positive

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{values}\:\mathrm{of}\:\:\mathrm{a}\:\:\mathrm{and}\:\:\mathrm{b} \\ $$$$\mathrm{such}\:\mathrm{that}\:\:\mathrm{y}=\mathrm{0},\mathrm{5x}^{\mathrm{2}} +\left(\mathrm{a}+\mathrm{b}\right)\mathrm{x}+\mathrm{ab} \\ $$$$\mathrm{is}\:\mathrm{always}\:\mathrm{positive} \\ $$

Question Number 167037    Answers: 2   Comments: 0

If I = ∫_(-1) ^( -8) (1/(x^(2/3) − x)) dx then what is the value of 81e^I ?

$$\mathrm{If}\:\:\:\:\:\mathrm{I}\:=\:\int_{-\mathrm{1}} ^{\:-\mathrm{8}} \:\frac{\mathrm{1}}{\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:−\:\mathrm{x}}\:\mathrm{dx} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{81}\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{I}}} \:? \\ $$

Question Number 167036    Answers: 1   Comments: 0

Evaluate: Ω = ∫ 620 (x^(2017) - 69 x^(126) )^(15) dx

$$\mathrm{Evaluate}: \\ $$$$\Omega\:=\:\int\:\mathrm{620}\:\left(\mathrm{x}^{\mathrm{2017}} \:-\:\mathrm{69}\:\mathrm{x}^{\mathrm{126}} \right)^{\mathrm{15}} \:\mathrm{dx} \\ $$

Question Number 167028    Answers: 1   Comments: 0

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

$$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{2x}}−\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{3x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 167027    Answers: 0   Comments: 1

Question Number 167025    Answers: 0   Comments: 0

∫_0 ^(π/3) (√(1−(1/(3 ))sin^2 θ)) dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{3}}} \sqrt{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}\:}\mathrm{sin}\:^{\mathrm{2}} \theta}\:\mathrm{d}\theta \\ $$

Question Number 167024    Answers: 1   Comments: 0

∫sec θtan^4 θdθ

$$\int\mathrm{sec}\:\theta\mathrm{tan}\:^{\mathrm{4}} \theta\mathrm{d}\theta \\ $$

Question Number 167021    Answers: 0   Comments: 0

how can it solve this ? (1)sin360 (2)tan345 (3)cos170 (4)sec150 (5)cot150

$${how}\:{can}\:{it}\:{solve}\:{this}\:? \\ $$$$ \\ $$$$\left(\mathrm{1}\right){sin}\mathrm{360} \\ $$$$\left(\mathrm{2}\right){tan}\mathrm{345} \\ $$$$\left(\mathrm{3}\right){cos}\mathrm{170} \\ $$$$\left(\mathrm{4}\right){sec}\mathrm{150} \\ $$$$\left(\mathrm{5}\right){cot}\mathrm{150} \\ $$

Question Number 167013    Answers: 1   Comments: 0

Question Number 167011    Answers: 2   Comments: 0

Question Number 167010    Answers: 1   Comments: 0

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