Test for vergances of fallowing Cor +oo Σ n=1 Jn² +n

Q: 7. Evaluate the Integral S (x + 3) dx

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Q: Evaluate the integral. S 20x cos x dx Select one: O A.80 sin. 1 40x cos + C O B.20 sin n1)x+ 40x cos…

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Q: 5. Σ S2 (Integral test) |3| V3n +2 n=1 PDT Provided to JoA

A: We use integral test

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

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Q: Evaluate the integral 1 2 s s хе dx dy -1

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: Q6) Compute the integral 3 1 dxp -з (х +2)3

A: Here we solve the given integral.

Q: 13. Consider the integral | - dx then (which statement(s) is/are correct): x2 - 4x (i) dx : x - 4x…

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Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

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Q: 5 2 +2 ) dx using Estimate I - n = 4 subintervals and (a) Left endpoints. (b) Right endnoints.

A: solution:-I=∫152x+2dx,     n=4f(x)=2x+2∆x=5-14=1(a) Left end pointI=∆xf(1)+f(2)+f(3)+f(4)…

Q: Two random processes are defined as X (t) = A . cos (ot + 0); Y (t) = A sin (ot + 0), where A and a…

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Q: If the têst is inconclusive, then say SO. 3* Σ k! k=1 If p = +o, enter "inty". i

A: Given query is to find series converges or diverges.

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: Prove that Jn (x) X good dx=1. n

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Q: FIAD THE OTER FIXF FUH aiON OF ĦF xauTF XHGUE X O SIn X =3

A: The given function is:sinX=35To find other five function

Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

A: use partial differentiation for finding the derivative.

Q: Integrates PDE SE ニー Zく Z8 te

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Q: Q5) Evaluate the integral 0.61-10 (6.73x + 4.3025 - 10- dx 2.316 • 10-11 122-10- Using trapezoidal…

A: The solution to the integral can be calculated using numerical methods. The formula for the…

Q: A random process is dėji process and a >0 is a constant. Find the PSD of Y (t) in terms of the…

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Q: ind E(X) and V(X) for 28(t) = 0.4e2t +0.6e¬3t. random variable X whose moment-generating function i…

A: It is an important part of statistics. It is widely used.

Q: Bi(n, p) and using the MGF compute Derive the moment generating function of X E[X] and Var[X].

A: Given,A random variable X~Bi(n,p)P(X=x)=nxpxqn-x    ;   X=0,1,2,.....nand q=1-p

Q: =Sin n dQ 2Q= 2. dt 10+2t

A: Given, a)y'+y=sinx b)dQdt+210+2tQ=4; Q(2)=100

Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. 9. 2² dx

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 1-cos(z) if 0 < z < ™ X has PDF f(1) = %3D .0 otherwise Find the probability P(0.64 < X < 2.76).

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Q: Evaluate the integral. 3y- cos xy dy dx x/3 O 5(1 - cos 3) O 3(1 - cos 3) O cos 3 -1 (1 cos 3)

A: Given: ∫03∫x313y2 cos xy dy dx We have x3≤y≤1 and 0≤x≤3 This can be seen as: We can change the…

Q: sell f G) unit ofitems af tersperding x houscin d on 9dverfising as given by fon) 5 n3 - 3 n2 +…

A: Given function is  f(x)=53x3-32x2+(5+32)xf(x)=53x3-32x2+14x To find out inflection points we need to…

Q: dx Use Simpson's method to evaluate o x² + 9 Hence estimate error.

A: In this question first, we have to evaluate the integral through normal integration and find the…

Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

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Q: 4 a2 Calculate the integral: dx (2² + 7)/2 4 Va2 + 7 a) Vz? + 7 +C + 4 ln V7 4 x b) O x + Vx² + 7 +…

A: From the given problem:   I=∫4x2x2+732dx ........(1)   Let,…

Q: Evaluate the integral. S2 15 - x2 if o < xs 3 3 if -3 sx S0 f(x) dx where f(x) = %3D

A: See step 2

Q: Suppose that the joint p.m.f. of Y and Y2 is defined by: 2x + y for x = 1, 2,3; y = 1,2,3 54 f(x, y)…

A: The probability mass function of Y1 and Y2 is,

Q: Q5) Use Simpson's 3/8 rule to compute the approximated solution 1 where f (x): defined at the…

A: The objective is to estimate solution of fx=1cosx+4x over the interval 1,4.5 and n=7 using Simpson's…

Q: En=1" Vn sin а. 1 b. 2 c. Converge

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Q: dx Use Simpson's method to evaluate o x² +9 Hence estimate error.

A: To evaluate ∫02dxx2+9, let n=4. The Simpson's rule says that…

Q: z'e? dz

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Q: 39. (a) Show that 1 1 > 0 2x V1+x² for x > 1. (b) Use your result in (a) to show that 1 dx 1+x is…

A: The compleet solutions are geven below

Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: III. Evaluate using simple divergence test cos(n7) п 6. n=0 2(n +1) Зп - 1 7.

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Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

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Q: Q1. Evaluate the integral S dx (x + 1)(x² + 1)

A: We need to evaluate the following integral ∫01dxx+1x2+1

Q: E valvate cox³ (x²+3)dx 2.

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Q: 2. S*3*+2 dx x+2

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Q: V312-x2 31 dydx = %3D 1+x2+y2 Jo int062) ○ 푸n(31) 2 O In(962) O TIn(962) O 2nln(31)

A: Given: I=∫031∫0312-x221+x2+y2dxydx   Now convert to polar coordinate to solve the given integral. As…

Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate:

Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.