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Question Number 167119 Answers: 1 Comments: 0

(z+3i)^(20) =?

$$\left({z}+\mathrm{3}{i}\right)^{\mathrm{20}} =? \\ $$

Question Number 167115 Answers: 0 Comments: 0

Question Number 167110 Answers: 1 Comments: 0

Find the remainder when:− (a) 41! is divided by 1681 (b) 225! is divided by 227 (c) 15! is divided by 19

$$\:\:{Find}\:{the}\:{remainder}\:{when}:− \\ $$$$\:\:\left({a}\right)\:\:\mathrm{41}!\:{is}\:{divided}\:{by}\:\mathrm{1681} \\ $$$$\:\:\left({b}\right)\:\mathrm{225}!\:{is}\:{divided}\:{by}\:\mathrm{227} \\ $$$$\:\:\left({c}\right)\:\mathrm{15}!\:{is}\:{divided}\:{by}\:\mathrm{19} \\ $$

Question Number 167107 Answers: 1 Comments: 0

Question Number 167105 Answers: 4 Comments: 0

If g(x)= { (( x^( 2) x≥1)),(( x^( 3) x< 1)) :} then lim_( h→ 0^( +) ) (( g (1+3h ) − g (1−5h ))/h) =?

$$ \\ $$$$\:\:\:\:\mathrm{I}{f}\:\:\:\:{g}\left({x}\right)=\:\begin{cases}{\:{x}^{\:\mathrm{2}} \:\:\:\:\:{x}\geqslant\mathrm{1}}\\{\:{x}^{\:\mathrm{3}} \:\:\:\:\:\:\:{x}<\:\mathrm{1}}\end{cases}\: \\ $$$$\:\:\:\:\:\:{then}\:\:\:\:\:{lim}_{\:{h}\rightarrow\:\mathrm{0}^{\:+} } \frac{\:{g}\:\left(\mathrm{1}+\mathrm{3}{h}\:\right)\:−\:{g}\:\left(\mathrm{1}−\mathrm{5}{h}\:\right)}{{h}}\:=? \\ $$

Question Number 167102 Answers: 0 Comments: 0

Ω = ∫_0 ^( 1) ((Li_( 2) (1− x ))/(1+x)) dx = ? −−−−−

$$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{Li}_{\:\mathrm{2}} \left(\mathrm{1}−\:{x}\:\right)}{\mathrm{1}+{x}}\:{dx}\:=\:? \\ $$$$\:\:\:\:\:\:−−−−− \\ $$

Question Number 167100 Answers: 1 Comments: 1

calculate :: lim_(x→0^+ ) ((∫_0 ^x cos^n ((1/t))dt)/x)=?

$$\mathrm{calculate}\:\:\:::\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{\int_{\mathrm{0}} ^{\mathrm{x}} \mathrm{cos}\:^{\mathrm{n}} \left(\frac{\mathrm{1}}{\mathrm{t}}\right)\mathrm{dt}}{\mathrm{x}}=? \\ $$

Question Number 167092 Answers: 0 Comments: 0

Question Number 167091 Answers: 0 Comments: 0

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

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 ?

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

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