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Question Number 103209 Answers: 3 Comments: 0

Question Number 103119 Answers: 0 Comments: 0

∫((log(((1+(√5))/2)(√x)−1))/(x^(√x) log(((1+(√5))/2)(√x)+1)−1))

$\int \frac{l o g (\frac{1 + \sqrt{5}}{2} \sqrt{x} - 1)}{x^{\sqrt{x}} l o g (\frac{1 + \sqrt{5}}{2} \sqrt{x} + 1) - 1}$

Question Number 103016 Answers: 0 Comments: 0

Question Number 103859 Answers: 1 Comments: 0

solve : y^2 + x^2 = −sin(θ) ., (π/2)≥ θ≥−(π/2)

$s o l v e :$ $y^{2} + x^{2} = - \sin (θ) ., \frac{π}{2} ⩾ θ ⩾ - \frac{π}{2}$

Question Number 102822 Answers: 1 Comments: 1

Σ_(n=1) ^∞ ((n!)/n^n )

$\underset{n = 1}{\sum^{\infty}} \frac{n!}{n^{n}}$

Question Number 102745 Answers: 0 Comments: 2

1−1+1−1+1−1+1−1+.....=(1/2) {But it diverges 1+1+1+1+1+1+1+......=−(1/2) {But it diverges 1+2+4+8+16+.....=−1 {But it diverges 1+2+3+4+5+6+7=−(1/(12)) {But it diverges 1−2+4−8+.....=(1/3) {But it diverges 1−2+3−4+5−6+.....=(1/4) {Is it a divergent?????

$1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + . . . . . = \frac{1}{2} {B u t i t d i v e r g e s$ $1 + 1 + 1 + 1 + 1 + 1 + 1 + . . . . . . = - \frac{1}{2} {B u t i t d i v e r g e s$ $1 + 2 + 4 + 8 + 16 + . . . . . = - 1 {B u t i t d i v e r g e s$ $1 + 2 + 3 + 4 + 5 + 6 + 7 = - \frac{1}{12} {B u t i t d i v e r g e s$ $1 - 2 + 4 - 8 + . . . . . = \frac{1}{3} {B u t i t d i v e r g e s$ $1 - 2 + 3 - 4 + 5 - 6 + . . . . . = \frac{1}{4} {I s i t a d i v e r g e n t ? ? ? ? ?$

Question Number 102701 Answers: 2 Comments: 1

Evaluate: ∫((sin x)/x)dx

$E v a l u a t e :$ $\int \frac{\sin x}{x} d x$

Question Number 102686 Answers: 0 Comments: 1

Σ_(r=1) ^∞ i^r +Σ_(r=0) ^∞ i^r

$\underset{r = 1}{\sum^{\infty}} i^{r} + \underset{r = 0}{\sum^{\infty}} i^{r}$

Question Number 102664 Answers: 2 Comments: 0

2x=5 x=? −−− for test app only

$2 x = 5$ $x = ?$ $- - -$ $f o r t e s t a p p o n l y$

Question Number 102651 Answers: 0 Comments: 1

12+14+24+58+164....upto nth terms

$12 + 14 + 24 + 58 + 164 . . . . upto nth terms$

Question Number 102635 Answers: 2 Comments: 0

Question Number 102627 Answers: 3 Comments: 0

show that: cosθ + cos2θ + ....cos nθ= ((cos (1/2)(n +1)θ sin(1/2)nθ)/(sin (1/2)nθ)) Show that: sin θ + sin 2θ + ....+ sin nθ = ((sin (1/2)(n + 1)θ sin(1/2)nθ)/(sin (1/2)nθ)) where θ ∈ R and θ ≠2πk , k ∈Z

$show that : \cos θ + \cos 2 θ + . . . . \cos n θ = \frac{\cos \frac{1}{2} (n + 1) θ \sin \frac{1}{2} n θ}{\sin \frac{1}{2} n θ}$ $Show that : \sin θ + \sin 2 θ + . . . . + \sin n θ = \frac{\sin \frac{1}{2} (n + 1) θ \sin \frac{1}{2} n θ}{\sin \frac{1}{2} n θ}$ $where θ \in R and θ \neq 2 π k, k \in Z$

Question Number 102598 Answers: 2 Comments: 0

Question Number 102545 Answers: 1 Comments: 0

Question Number 102544 Answers: 2 Comments: 0

Question Number 102539 Answers: 3 Comments: 2

2+3.3+4.3^2 +5.3^2 +.....up to n terms

$2 + 3.3 + 4 . 3^{2} + 5 . 3^{2} + . . . . . u p t o n t e r m s$

Question Number 102530 Answers: 0 Comments: 1

Question Number 102484 Answers: 1 Comments: 0

Question Number 102407 Answers: 0 Comments: 0

Sir MJS & Sir John Santu You both have decided to leave this forum for different reasons. Being agree with your reasons and accepting your right of decision I dare to suggest not to disconnect fully from the forum.Please stay connected although for very short time on daily/weekly basis.This is also necessary because we have no means to contact you. After all this is only a request. You may or may not accept it.

$Sir MJS & Sir John Santu$ $Y o u b o t h h a v e d e c i d e d t o l e a v e$ $t h i s f o r u m f o r d i f f e r e n t r e a s o n s .$ $B e i n g a g r e e w i t h y o u r r e a s o n s$ $a n d a c c e p t i n g y o u r r i g h t o f$ $d e c i s i o n I d a r e t o s u g g e s t n o t$ $t o d i s c o n n e c t f u l l y f r o m t h e$ $f o r u m . P l e a s e s t a y c o n n e c t e d$ $a l t h o u g h f o r v e r y s h o r t t i m e o n$ $d a i l y / w e e k l y b a s i s . T h i s i s a l s o$ $n e c e s s a r y b e c a u s e w e h a v e n o$ $m e a n s t o c o n t a c t y o u .$ $A f t e r a l l t h i s i s o n l y a r e q u e s t .$ $Y o u m a y o r m a y n o t a c c e p t i t .$

Question Number 102362 Answers: 0 Comments: 0

please how calculate the development limity of f(x,y)=x^y ,take a( 3,2) at order one and two

$p l e a s e h o w c a l c u l a t e t h e d e v e l o p m e n t l i m i t y o f f (x, y) = x^{y}$ $, t a k e a (3, 2) a t o r d e r o n e a n d t w o$

Question Number 102336 Answers: 1 Comments: 1

if f(x)≤2l +1 and ∫_1 ^3 f(x)dx≤l^2 find the value of l

$i f f (x) ⩽ 2 l + 1$ $a n d \int_{1}^{3} f (x) d x ⩽ l^{2}$ $f i n d t h e v a l u e o f l$

Question Number 102142 Answers: 0 Comments: 0

A four-sidex dice with numbered 1, 2, 3, and 4 is thrown and the number at the base is read. The dice is biased such that the probabilies P_1 , P_2 , P_3 , and P_4 to obtain 1, 2, 3, and 4 respectively are in an arithmetic progression. 1\ Given P_4 =0.4, calculate P_1 , P_2 , and P_3 . 2\ The dice is thrown n-times (n≥1). The throws are assumed to be independent, 2 by 2, and identical. Given U_n -the probability of obtaining for the first time the fourth-n^(th) throw; a\Express U_n in terms of n= b\Given S_n =Σ_(i=1) ^n U_i i. Express Sn in terms of n, and find its limit. ii. Determine the smallest natural number such that S_n >0.999

$A four - sidex dice with numbered 1, 2, 3, and 4 is thrown$ $and the number at the base is read .$ $The dice is biased such that the probabilies P_{1}, P_{2}, P_{3},$ $and P_{4} to obtain 1, 2, 3, and 4 respectively are in an$ $arithmetic progression .$ $1 ∖ Given P_{4} = 0.4, calculate P_{1}, P_{2}, and P_{3} .$ $2 ∖ The dice is thrown n - times (n ⩾ 1) . The throws are assumed$ $to be independent, 2 by 2, and identical . Given U_{n} - the probability$ $of obtaining for the first time the fourth - n^{th} throw;$ $a ∖ Express U_{n} in terms of n =$ $b ∖ Given S_{n} = \underset{i = 1}{\sum^{n}} U_{i}$ $i . Express Sn in terms of n, and find its limit .$ $ii . Determine the smallest natural number such that$ $S_{n} > 0.999$

Question Number 102089 Answers: 2 Comments: 0

The Gamma function Γ(α) is defined as follows; Γ(α)=∫_0 ^∞ y^(α−1) e^(−y) dy , α>0 a\ Show that Γ(α+1)=αΓ(α). b\Conclude that Γ(n)=(n−1)! , n=1, 2, 3, ... c\Determine Γ(55).

$The Gamma function Γ (α) is defined as follows;$ $Γ (α) = \int_{0}^{\infty} y^{α - 1} e^{- y} dy, α > 0$ $a ∖ Show that Γ (α + 1) = α Γ (α) .$ $b ∖ Conclude that Γ (n) = (n - 1)!, n = 1, 2, 3, . . .$ $c ∖ Determine Γ (55) .$

Question Number 102085 Answers: 0 Comments: 0

Question Number 102080 Answers: 0 Comments: 0

A random variable, X, has a Gamma distribution with parameters α and β, (α, β>0). The p.d.f has the form f(x)=(1/(Γ(α)β^α ))x^(n−1) e^(−x/β) , for x>0 , Γ(α)=(1/β^α )∫_0 ^∞ x^(α−1) e^(−x) dx a\ Show that the Gamma density is a proper p.d.f. b\Find the mean, variance, and moment-generating function of the Gamma distribution. c\Find the fourth moment using the definition of moments.

$A random variable, X, has a Gamma distribution with$ $parameters α and β, (α, β > 0) . The p . d . f has the form$ $f (x) = \frac{1}{Γ (α) β^{α}} x^{n - 1} e^{- x / β}, for x > 0, Γ (α) = \frac{1}{β^{α}} \int_{0}^{\infty} x^{α - 1} e^{- x} dx$ $a ∖ Show that the Gamma density is a proper p . d . f .$ $b ∖ Find the mean, variance, and moment - generating function of$ $the Gamma distribution .$ $c ∖ Find the fourth moment using the definition of moments .$

Question Number 102076 Answers: 0 Comments: 4

A car is currently valued at $70350.00. If it loses 12% of its value at the beginning of each year, a) find its value after three and half years. b) find the depreciation after three years

$A car is currently valued at $ 70350.00 .$ $If it loses 12 % of its value at the beginning$ $of each year,$ $a) find its value after three and half years .$ $b) find the depreciation after three years$

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