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AllQuestion and Answers: Page 359

Question Number 182838 Answers: 0 Comments: 0

Question Number 182836 Answers: 2 Comments: 0

Question Number 182835 Answers: 1 Comments: 0

s(n)=Σ_(n=1) ^(+oo) (((−1)^n +n^2 )/(n!))x^n =?

$${s}\left({n}\right)=\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{n}} \:+{n}^{\mathrm{2}} }{{n}!}{x}^{{n}} \:=? \\ $$

Question Number 182829 Answers: 3 Comments: 0

Question Number 182811 Answers: 0 Comments: 0

Question Number 182810 Answers: 2 Comments: 0

What is the value of this infinite sum ((1/2)−(1/3))+((1/2^2 )−(1/3^2 ))+((1/2^3 )−(1/3^3 ))+...

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{this}\:\mathrm{infinite}\:\mathrm{sum} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)+\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }\right)+... \\ $$$$ \\ $$$$ \\ $$

Question Number 182809 Answers: 0 Comments: 0

Question Number 182804 Answers: 2 Comments: 0

solve ⌊x_ ^ ⌋ − ⌊ (x/3) ⌋ = 3

$$ \\ $$$$\:\:\:\:{solve} \\ $$$$\:\:\:\:\lfloor\underset{} {\overset{} {{x}}}\:\rfloor\:−\:\lfloor\:\frac{{x}}{\mathrm{3}}\:\rfloor\:=\:\mathrm{3} \\ $$$$\:\:\:\:\:\:\: \\ $$

Question Number 182803 Answers: 0 Comments: 0

write an 8085 mp assembly language program to separate even numbers from a list of 10 numbers and store them in another list starting from (2300H). assume starting address of 10 numbers list is (2200H).

$${write}\:{an}\:\mathrm{8085}\:{mp}\:{assembly}\:{language}\:{program} \\ $$$${to}\:{separate}\:{even}\:{numbers}\:{from}\:{a}\:{list}\:{of} \\ $$$$\mathrm{10}\:{numbers}\:{and}\:{store}\:{them}\:{in}\:{another} \\ $$$${list}\:{starting}\:{from}\:\left(\mathrm{2300}{H}\right).\:{assume}\:{starting} \\ $$$${address}\:{of}\:\mathrm{10}\:{numbers}\:{list}\:{is}\:\left(\mathrm{2200}{H}\right). \\ $$

Question Number 182797 Answers: 0 Comments: 1

find the max and min value f(x,y,z) = x^3 +y^3 +z^3 −9xy−9xz+27x

$$\:\mathrm{find}\:\:\mathrm{the}\:\mathrm{max}\:\mathrm{and}\:\:\mathrm{min}\:\mathrm{value} \\ $$$$\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} −\mathrm{9xy}−\mathrm{9xz}+\mathrm{27x} \\ $$

Question Number 182794 Answers: 1 Comments: 0

Ω = Σ_(n=1) ^∞ (( (−1_ ^ )^( n) )/(2^( n) .n(n+_ ^ 1)(n+_ ^ 2))) = ?

$$ \\ $$$$\:\:\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\:\left(−\underset{} {\overset{} {\mathrm{1}}}\:\right)^{\:{n}} }{\mathrm{2}^{\:{n}} .{n}\left({n}\underset{} {\overset{} {+}}\mathrm{1}\right)\left({n}\underset{} {\overset{} {+}}\mathrm{2}\right)}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 182791 Answers: 2 Comments: 0

We have 0<x<a and m,n ∈N. Prove x^m (a−x)^n ≤ ((m^m n^n )/((m+n)^(m+n) ))∙a^(m+n)

$$\:{We}\:{have}\:\mathrm{0}<{x}<{a}\:{and}\:{m},{n}\:\in\mathbb{N}. \\ $$$$\:{Prove}\:{x}^{{m}} \left({a}−{x}\right)^{{n}} \leqslant\:\frac{{m}^{{m}} {n}^{{n}} }{\left({m}+{n}\right)^{{m}+{n}} }\centerdot{a}^{{m}+{n}} \\ $$

Question Number 182788 Answers: 1 Comments: 0

y′′+ay=b

$${y}''+{ay}={b} \\ $$

Question Number 182786 Answers: 2 Comments: 0

existant and value m≥1 of S_m =Σ_(n=1 ^ ) ^(+oo) (1/(n(n+1)...(n+m)))

$${existant}\:{and}\:{value}\:{m}\geqslant\mathrm{1}\:{of} \\ $$$${S}_{{m}} =\underset{{n}=\mathrm{1}\:\overset{} {\:}} {\overset{+{oo}} {\sum}}\frac{\mathrm{1}}{{n}\left({n}+\mathrm{1}\right)...\left({n}+{m}\right)}\: \\ $$

Question Number 182779 Answers: 4 Comments: 1

Question Number 182772 Answers: 1 Comments: 0

χ { ((x= t+1)),((y= 2t−3)),((z= −t +2)) :} Δ { ((x= 3t +2)),((y= −t−1 )),((z= t+1)) :} { ((Are these two lines located)),((in the same plane or not?)),((where t∈ R)) :}

$$\:\chi\:\begin{cases}{{x}=\:{t}+\mathrm{1}}\\{{y}=\:\mathrm{2}{t}−\mathrm{3}}\\{{z}=\:−{t}\:+\mathrm{2}}\end{cases}\:\:\:\Delta\begin{cases}{{x}=\:\mathrm{3}{t}\:+\mathrm{2}}\\{{y}=\:−{t}−\mathrm{1}\:\:\:}\\{{z}=\:{t}+\mathrm{1}}\end{cases}\:\begin{cases}{{Are}\:\:{these}\:{two}\:{lines}\:{located}}\\{{in}\:{the}\:{same}\:{plane}\:{or}\:{not}?}\\{{where}\:{t}\in\:\mathbb{R}}\end{cases} \\ $$$$ \\ $$

Question Number 182771 Answers: 1 Comments: 7

∫ _0^r (1/(R^2 −r^2 ))dr=?

$$\int\:_{\mathrm{0}} ^{{r}} \:\frac{\mathrm{1}}{{R}^{\mathrm{2}} −{r}^{\mathrm{2}} }{dr}=? \\ $$

Question Number 182770 Answers: 1 Comments: 0

Question Number 182769 Answers: 1 Comments: 0

∫_0 ^(π/4) (dx/(sin (x−1)−1)) =?

$$\:\:\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\frac{{dx}}{\mathrm{sin}\:\left({x}−\mathrm{1}\right)−\mathrm{1}}\:=?\: \\ $$

Question Number 182793 Answers: 0 Comments: 0

Suppose now that Allie is actually 70 years old, and that her life expectancy (if cured) is 12 years rather than 20 . Which procedure now has the greather expected value ? What if her life expectancy is 8 years?

$$\:{Suppose}\:{now}\:{that}\:{Allie}\:{is}\:{actually} \\ $$$$\mathrm{70}\:{years}\:{old},\:{and}\:{that}\:{her}\:{life}\:{expectancy} \\ $$$$\left({if}\:{cured}\right)\:{is}\:\mathrm{12}\:{years}\:{rather}\:{than} \\ $$$$\mathrm{20}\:.\:{Which}\:{procedure}\:{now}\:{has}\:{the} \\ $$$${greather}\:{expected}\:{value}\:?\:{What}\:{if}\:{her} \\ $$$${life}\:{expectancy}\:{is}\:\mathrm{8}\:{years}? \\ $$

Question Number 182737 Answers: 1 Comments: 0

Question Number 182726 Answers: 2 Comments: 4

∫_0 ^1 t(√((1−t)/(1+t)))dt=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \:{t}\sqrt{\frac{\mathrm{1}−{t}}{\mathrm{1}+{t}}}{dt}=? \\ $$

Question Number 182720 Answers: 0 Comments: 0

Question Number 182721 Answers: 2 Comments: 0

Question Number 182718 Answers: 2 Comments: 4

If , 7^( n) ≡^(10) 7^( 19) then find the 1st digit of the numer , 8^( n+4) .

$$ \\ $$$$\:\:\:\:\:\:\mathrm{If}\:,\:\:\:\:\mathrm{7}^{\:{n}} \:\overset{\mathrm{10}} {\equiv}\:\mathrm{7}^{\:\mathrm{19}} \\ $$$$\:\:\:\:\:\:\:{then}\:\:{find}\:{the}\:\:\mathrm{1}{st}\:{digit} \\ $$$$\:\:\:\:{of}\:\:{the}\:{numer}\:\:,\:\:\:\mathrm{8}^{\:{n}+\mathrm{4}} \:.\: \\ $$$$\:\:\:\:\:\:\:\: \\ $$

Question Number 182716 Answers: 1 Comments: 0

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