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Question Number 186680 Answers: 0 Comments: 0

study the convergence of: Σ_(n=1) ^(+∞) Π_(k=1) ^n (1−e^(((1/k))) )

$${study}\:{the}\:{convergence}\:{of}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\left(\mathrm{1}−{e}^{\left(\frac{\mathrm{1}}{{k}}\right)} \right) \\ $$

Question Number 186667 Answers: 2 Comments: 0

Question Number 186666 Answers: 0 Comments: 0

a,b>0 , a+b=2 Prove that a^(2b) +b^(2a) +(((a−b)/2))^2 ≤2

$$\mathrm{a},\mathrm{b}>\mathrm{0}\:,\:\mathrm{a}+\mathrm{b}=\mathrm{2} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2b}} +\mathrm{b}^{\mathrm{2a}} +\left(\frac{\mathrm{a}−\mathrm{b}}{\mathrm{2}}\right)^{\mathrm{2}} \leqslant\mathrm{2} \\ $$

Question Number 186675 Answers: 2 Comments: 0

Question Number 186662 Answers: 1 Comments: 0

Question Number 186659 Answers: 0 Comments: 1

find the value a and b if lim_(x→0) (((sin 2x)/x^2 ) +a+(b/x^2 ))=0

$${find}\:{the}\:{value}\:{a}\:{and}\:{b}\:{if}\: \\ $$$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{2}} }\:+{a}+\frac{{b}}{{x}^{\mathrm{2}} }\right)=\mathrm{0} \\ $$

Question Number 186732 Answers: 2 Comments: 0

Question Number 186657 Answers: 1 Comments: 0

Question Number 186647 Answers: 0 Comments: 2

Due to Earth's rotation. celestial objects like the moon and the stars appear to move across the sky, rising in the East and setting in the West. As a result, if a telescope on the Earth remains stationary while viewing a celestial object, the object will slowly move outside the viewing field of the telescope. For this reason, a motor is often attached to telescopes so that the telescope rotates at the same rate as the Earth. Determine how long it should take the motor to turn the telescope through an angle of 1min in a direction perpendicular to Earth's axis.

$$ \\ $$Due to Earth's rotation. celestial objects like the moon and the stars appear to move across the sky, rising in the East and setting in the West. As a result, if a telescope on the Earth remains stationary while viewing a celestial object, the object will slowly move outside the viewing field of the telescope. For this reason, a motor is often attached to telescopes so that the telescope rotates at the same rate as the Earth. Determine how long it should take the motor to turn the telescope through an angle of 1min in a direction perpendicular to Earth's axis.

Question Number 186645 Answers: 2 Comments: 1

Question Number 186617 Answers: 1 Comments: 2

lim_(x→∞) ((x^2 −1)/( (((x^2 −1)))^(1/5) ))=? with solution

$$\underset{{x}\rightarrow\infty} {{lim}}\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\:\sqrt[{\mathrm{5}}]{\left({x}^{\mathrm{2}} −\mathrm{1}\right)}}=?\:\:\:\:\:\:\:\:{with}\:{solution} \\ $$

Question Number 186616 Answers: 1 Comments: 0

Question Number 186613 Answers: 0 Comments: 0

Question Number 186622 Answers: 1 Comments: 2

Solve plz ((√(4+3(√(25+4(√(16)))))))^2

$$\:\:\:\mathrm{Solve}\:\mathrm{plz} \\ $$$$\:\:\:\:\left(\sqrt{\mathrm{4}+\mathrm{3}\sqrt{\mathrm{25}+\mathrm{4}\sqrt{\mathrm{16}}}}\right)^{\mathrm{2}} \\ $$

Question Number 186605 Answers: 1 Comments: 1

Question Number 186637 Answers: 2 Comments: 0

Question Number 186636 Answers: 1 Comments: 2

x^2 +x+1=0 x^(92) =?

$${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:{x}^{\mathrm{92}} =? \\ $$

Question Number 186631 Answers: 1 Comments: 2

Question Number 186630 Answers: 1 Comments: 0

Question Number 186627 Answers: 2 Comments: 1

Question Number 186590 Answers: 3 Comments: 0

A+B=(π/4) find the (1+tanA)(1+tanB)=? with explanotory solution

$$\mathrm{A}+\mathrm{B}=\frac{\pi}{\mathrm{4}}\:\:\:\:\:{find}\:{the}\:\left(\mathrm{1}+\mathrm{tan}{A}\right)\left(\mathrm{1}+\mathrm{tan}{B}\right)=?\: \\ $$$${with}\:{explanotory}\:{solution} \\ $$

Question Number 186582 Answers: 0 Comments: 0

(((10x^3 −c)/(4x^4 −x+1))+x^2 )^2 =x(x^3 +1)

$$\left(\frac{\mathrm{10}{x}^{\mathrm{3}} −{c}}{\mathrm{4}{x}^{\mathrm{4}} −{x}+\mathrm{1}}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} ={x}\left({x}^{\mathrm{3}} +\mathrm{1}\right) \\ $$

Question Number 186580 Answers: 0 Comments: 0

∫_0 ^1 e^x^2 dx=A ,Find lim_(n→∞) n[(1/n)Σ_(i=1) ^n ∫_1 ^(i/n) e^x^2 dx+((e−1)/2)]=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} {e}^{{x}^{\mathrm{2}} } {dx}={A}\:\:,{Find}\:\underset{{n}\rightarrow\infty} {{lim}n}\left[\frac{\mathrm{1}}{{n}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\int_{\mathrm{1}} ^{{i}/{n}} {e}^{{x}^{\mathrm{2}} } {dx}+\frac{{e}−\mathrm{1}}{\mathrm{2}}\right]=? \\ $$

Question Number 186577 Answers: 1 Comments: 0

Question Number 186572 Answers: 1 Comments: 0

f={(1,2),(4,6),(5,8)} and g={(1,7),(2,4),(5,8)} the domain of f(g(x)) which number is not include? 1)1 2)2 3)5 4)all corect how is the solution?

$${f}=\left\{\left(\mathrm{1},\mathrm{2}\right),\left(\mathrm{4},\mathrm{6}\right),\left(\mathrm{5},\mathrm{8}\right)\right\}\:\:{and}\:\:\:{g}=\left\{\left(\mathrm{1},\mathrm{7}\right),\left(\mathrm{2},\mathrm{4}\right),\left(\mathrm{5},\mathrm{8}\right)\right\} \\ $$$${the}\:{domain}\:{of}\:\:\:{f}\left({g}\left({x}\right)\right)\:\:\:{which}\:{number}\:{is}\:{not}\:{include}? \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{1}\left.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\right){all}\:{corect} \\ $$$${how}\:{is}\:{the}\:{solution}? \\ $$

Question Number 186571 Answers: 2 Comments: 0

If x=−(1/((1+m)))((2/3)±(√((4/9)±((ia(√m))/(12))))) where (1+m)^2 =am and that 9a(a+16)^2 =(16)^3 Find real x.

$${If}\:\:\:{x}=−\frac{\mathrm{1}}{\left(\mathrm{1}+{m}\right)}\left(\frac{\mathrm{2}}{\mathrm{3}}\pm\sqrt{\frac{\mathrm{4}}{\mathrm{9}}\pm\frac{{ia}\sqrt{{m}}}{\mathrm{12}}}\right) \\ $$$${where}\:\:\:\left(\mathrm{1}+{m}\right)^{\mathrm{2}} ={am} \\ $$$$\:\:\:\:{and}\:{that}\:\:\mathrm{9}{a}\left({a}+\mathrm{16}\right)^{\mathrm{2}} =\left(\mathrm{16}\right)^{\mathrm{3}} \\ $$$${Find}\:{real}\:{x}. \\ $$

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