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Question Number 28808 Answers: 2 Comments: 0

Question Number 28806 Answers: 1 Comments: 0

If n(A)=15 and n(B)=25, (a) What are the greatest and least values of n(AuB)? (b) What are the greatest and least value of n(AnB)? (c) Draw Venn diagrams to illustrate the four situations in (a) and (b) above

$$\mathrm{If}\:\mathrm{n}\left(\mathrm{A}\right)=\mathrm{15}\:\mathrm{and}\:\mathrm{n}\left(\mathrm{B}\right)=\mathrm{25},\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\left(\mathrm{AuB}\right)? \\ $$$$\left(\mathrm{b}\right)\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{and}\:\mathrm{least}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\left(\mathrm{AnB}\right)? \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Draw}\:\mathrm{Venn}\:\mathrm{diagrams}\:\mathrm{to}\:\mathrm{illustrate}\:\mathrm{the}\:\mathrm{four}\: \\ $$$$\:\:\:\:\:\:\:\mathrm{situations}\:\mathrm{in}\:\left(\mathrm{a}\right)\:\mathrm{and}\:\left(\mathrm{b}\right)\:\mathrm{above} \\ $$

Question Number 28805 Answers: 1 Comments: 0

In a competition, a school awarded medals in different categories. 36 medals in dance,12 in dramatics and 18 medals in music.If these medals went to total 45,and only 4 persons got medals in all three catogories.Using set notations, how many received in exactly two of these categories?

$${In}\:{a}\:{competition},\:{a}\:{school}\:{awarded} \\ $$$${medals}\:{in}\:{different}\:{categories}. \\ $$$$\mathrm{36}\:{medals}\:{in}\:{dance},\mathrm{12}\:{in}\:{dramatics} \\ $$$${and}\:\mathrm{18}\:{medals}\:{in}\:{music}.{If}\:{these} \\ $$$${medals}\:{went}\:{to}\:{total}\:\mathrm{45},{and}\:{only} \\ $$$$\mathrm{4}\:{persons}\:{got}\:{medals}\:{in}\:{all}\:{three} \\ $$$${catogories}.{Using}\:{set}\:{notations}, \\ $$$${how}\:{many}\:{received}\:{in}\:{exactly} \\ $$$${two}\:{of}\:{these}\:{categories}? \\ $$

Question Number 28779 Answers: 3 Comments: 1

Question Number 28770 Answers: 1 Comments: 6

lim_(x→+∞) ((5x^4 −10x^2 +1)/(−3x^3 +10x^2 +50))

$$\underset{{x}\rightarrow+\infty} {{lim}}\:\frac{\mathrm{5}{x}^{\mathrm{4}} −\mathrm{10}{x}^{\mathrm{2}} +\mathrm{1}}{−\mathrm{3}{x}^{\mathrm{3}} +\mathrm{10}{x}^{\mathrm{2}} +\mathrm{50}} \\ $$

Question Number 28762 Answers: 1 Comments: 6

Question Number 28739 Answers: 1 Comments: 0

if S_n =((a(r^n −1))/(r−1)) make r the subject of formula

$${if}\:{S}_{{n}} =\frac{{a}\left({r}^{{n}} −\mathrm{1}\right)}{{r}−\mathrm{1}}\: \\ $$$$ \\ $$$${make}\:{r}\:{the}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 28709 Answers: 1 Comments: 0

Question Number 28708 Answers: 0 Comments: 0

If θ = log_e {tan(((3π)/8))} , prove that 3 tanh(2θ) = 2(√2)

$$\mathrm{If}\:\:\:\theta\:\:=\:\:\mathrm{log}_{\mathrm{e}} \left\{\mathrm{tan}\left(\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\right\}\:,\:\:\:\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}\:\mathrm{tanh}\left(\mathrm{2}\theta\right)\:=\:\mathrm{2}\sqrt{\mathrm{2}} \\ $$

Question Number 28706 Answers: 1 Comments: 7

most important question gor boar or iit solve the integration (1/(3sinx+4cosx))

$${most}\:{important}\:{question}\:{gor}\:{boar}\:{or}\:{iit}\: \\ $$$${solve}\:{the}\:{integration}\:\:\frac{\mathrm{1}}{\mathrm{3}{sinx}+\mathrm{4}{cosx}} \\ $$

Question Number 28705 Answers: 1 Comments: 0

solve the integrayion ((sin2x)/(sin5xsin3x))

$${solve}\:{the}\:{integrayion}\:\frac{{sin}\mathrm{2}{x}}{{sin}\mathrm{5}{xsin}\mathrm{3}{x}} \\ $$

Question Number 28703 Answers: 0 Comments: 1

(1/((a^2 +x^2 )^(3/2) )) solve the integration

$$\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\:\:{solve}\:{the}\:{integration} \\ $$

Question Number 28702 Answers: 0 Comments: 1

solve integration (1/(√((x−α)(β−x)))) .

$${solve}\:{integration}\:\:\frac{\mathrm{1}}{\sqrt{\left({x}−\alpha\right)\left(\beta−{x}\right)}}\:\:. \\ $$

Question Number 28701 Answers: 1 Comments: 2

integration (x^3 /(x^2 +x+1))

$${integration}\:\frac{{x}^{\mathrm{3}} }{{x}^{\mathrm{2}} +{x}+\mathrm{1}} \\ $$

Question Number 28700 Answers: 0 Comments: 0

solve integration (√((sin(x−α))/(sin(x+α))))

$${solve}\:{integration}\:\sqrt{\frac{{sin}\left({x}−\alpha\right)}{{sin}\left({x}+\alpha\right)}} \\ $$

Question Number 28698 Answers: 0 Comments: 3

(∞/(negative number))=? ∞ or −∞ ?

$$\frac{\infty}{\mathrm{negative}\:\mathrm{number}}=? \\ $$$$\:\infty\:\:\:\:\:\:\:\:\:\:\mathrm{or}\:\:\:\:\:\:\:\:\:−\infty\:\:? \\ $$

Question Number 28695 Answers: 1 Comments: 0

∣a^→ +b^→ ∣=40,∣a^→ −b^→ ∣=20&∣a^→ ∣=10 then find∣b^→ ∣

$$\mid\overset{\rightarrow} {\mathrm{a}}+\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{40},\mid\overset{\rightarrow} {\mathrm{a}}−\overset{\rightarrow} {\mathrm{b}}\mid=\mathrm{20\&}\mid\overset{\rightarrow} {\mathrm{a}}\mid=\mathrm{10}\:\mathrm{then}\:\mathrm{find}\mid\overset{\rightarrow} {\mathrm{b}}\mid \\ $$

Question Number 28694 Answers: 0 Comments: 1

find the value of ∫_0 ^∞ e^(−tx^2 ) cosx dx with t>0 .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{tx}^{\mathrm{2}} } {cosx}\:{dx}\:\:{with}\:{t}>\mathrm{0}\:. \\ $$

Question Number 28690 Answers: 0 Comments: 5

Question Number 28687 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−( t^2 +(1/t^2 ))) dt.

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\left(\:{t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right)} {dt}. \\ $$

Question Number 28685 Answers: 0 Comments: 0

find the value of I=∫∫_D x^3 dxdy with D= {(x,y)∈R^2 /1≤x≤2 and x^2 −y^2 ≥1 }.

$${find}\:{the}\:{value}\:{of}\:\:{I}=\int\int_{{D}} \:{x}^{\mathrm{3}} {dxdy}\:\:\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:{and}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\geqslant\mathrm{1}\:\:\right\}. \\ $$

Question Number 28684 Answers: 0 Comments: 0

find sum of S(x)= Σ_(n=1) ^∞ (−1)^(n−1) (x^(2n+1) /(4n^2 −1)) .

$${find}\:\:{sum}\:{of}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}}\:. \\ $$

Question Number 28683 Answers: 0 Comments: 1

developp f(x)=e^(−αx) 2π periodic at Fourier serie with α>0.

$${developp}\:{f}\left({x}\right)={e}^{−\alpha{x}} \:\:\:\mathrm{2}\pi\:{periodic}\:{at}\:{Fourier}\:{serie}\:{with} \\ $$$$\alpha>\mathrm{0}. \\ $$

Question Number 28682 Answers: 0 Comments: 2

nature of the serie Σ_(n=0) ^∞ tan(((2n+1)/n^3 )) .

$${nature}\:{of}\:{the}\:{serie}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{tan}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{{n}^{\mathrm{3}} }\right)\:. \\ $$

Question Number 28681 Answers: 0 Comments: 0

give a equivalent of w_n = Σ_(k=n+1) ^∞ (1/(k!)) .

$${give}\:{a}\:{equivalent}\:{of}\:\:{w}_{{n}} =\:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{k}!}\:\:. \\ $$

Question Number 28680 Answers: 0 Comments: 0

find lim_(ξ→0) ∫_0 ^(π/2) (dx/(√(sin^2 x +ξcos^2 x))) .

$${find}\:\:{lim}_{\xi\rightarrow\mathrm{0}} \:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\:\frac{{dx}}{\sqrt{{sin}^{\mathrm{2}} {x}\:+\xi{cos}^{\mathrm{2}} {x}}}\:\:\:\:\:. \\ $$

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