6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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Q: 2. (i) Show that for a discrete dis.ribution B2> 1. (ii) Show that B2> B1

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Q: 10. dr S f(æ) dx = Choose...

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Q: 2) Use the antiderivative to find the exact answer for (hint u=3x) 1+9x²

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Q: O s/Vn 12

A: The standard error is denoted by SE

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A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: 5. Find the on the interval [0, 4]

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Q: Show that cl S = SU(Bd S) %3D

A: LetS⊆R, claim: closure(S)=S∪Bd S =S ∪ S' by definition bd(S) ={ x∈ℝ/x∉S° & x∉(ℝ-S)°} let  x∈S∪S'…

Q: 5. prove thatS" erf (x) dx =o CA

A: ddx(erf(x)) =2 e-x2π   I =∫-aa erf(x) dxI= erf(x) x -∫ ddxerf(x) x dxI = x erf(x) -2π∫ x e-x2 dx-x2…

Q: which of the folowiny -xト! is -3x 2 へ pove seies fore =e.e e E (-)"(-3x) n ハン 0 37 B. e (3x)" nこO *ス…

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Q: 2etūsw ER' such that and iov-2.Than (3ü)(B)

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Q: n) the Integral evalu ate car 1- (X² +3) e Xdx

A: Given integral Apply integration by parts formula to integrate

Q: Suppose that x̅ = 12, Sx = 2, and z is 1. what is X?

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Q: Q1. Compute xdx x'+10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: The given integral is, I=∫01xdxx3+10 Dividing the interval (0,1)  into 2 intervals (for 3 points)…

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: れお! /0 fi23)=4 4 (か) 2,十 F) Eanals it Ofiles)= 12 D Not if tha above

A: Given: Fx,y = x3y2 To find: Fx2,3 We know that Fxx,y is differentiation of Fx,y with respect to x ,…

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

Q: 2) Eliminate the arbitrary enstant, 4 y= x*+ Cix + Cz e-X

A: Given problem:- Eliminate the arbitrary constants. of y= x² + C₁x + C₂ e-x

Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

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Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: (-1)" -Σ S. n=1 Vn+1

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Q: 3 In ADU DDL =9mm. Z/=6mmand //=N". Find FD. 3

A: By using the cosine rule we can can find the third side of triangle if we have given the two sides…

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: Find the Gomplex sdutiona to the e/s 4. (You maly expres the latems in Gmiblex Polat fom).

A: We need to find the complex solutions corresponding to z4-[(1+i)/√2]=0. The solution needed to be…

Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

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Q: 3 1-Vy dy 2 2у3

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (8) If w = 5x² + 2y², x= -3s+t, and y = s – 4t. Find and Əw as

A: The objective is to find the partial derivatives .

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: Q1. Compute xdx x' +10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: we have  I=∫01x dxx3+10dx  n=3h=b-an=1-03=13…

Q: Thene m for Voritly functiom Mean Valne fex) 2. 3X -4 +S the

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Q: Please see the attached problem. Thanks!

A: Given:

Q: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

A: Given that x, n∈N and n≠0. According to question, N=0,1,2,3,4,5........ First suppose xn is positive…

Q: 火2sin C&) for ダチo fcx) = { for x =0 show that Con tinods or not

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Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm & integration formula of sech(x)

Q: What is the best substitution to make to evaluate S O u = 3x Ou = e³x u=1+e³x Ou = e-3x e³x 1+e³x dx…

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Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: 9 show Itat Ihe maclayvin Sevies For Hense is メ+ メ t.. 4- X

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Q: What are the value for sup e-* = е x>0 and inf e * - = XER

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Q: If [ In(ax)dx = 3, then a %3D 1

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Q: Use the Midpoint rule to deterine the Intergral for the error Function (erf)(belou) 4caurete to…

A: ∫01e-x2dx here we can take 4 interpolation point so n=4 so h = (1-0)/4 = 0.25 x0=0 x1=0.25 x2=0.5…

Q: 13. If w(x,y) = In(1+xy²), show that 2wxx + y³Wyx = 0. %3|

A: Given: w(x, y)=ln(1+xy2)  To show: 2wxx+y3wyx=0 Chain rule : ddx(f(g(x))=f'(g(x))g'(x) Quotient…

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x