4 Σ E Vn +1 n=-1

Q: f(x) * a = 49 (2n – 1)! 2". 72n + 1 + (x – 49)" n = 1 1 ㅇ윽+>m.72n+ 1.n! 1 (x - 49)" n = 0 1 1:3.5.…

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Q: 0.08e p'(z) = p'(z) = 0.08(- ( p(z) %3D 0.08(느 p'(z) = 0.08(-

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Q: 4. Suppose is a discrete rv with E(9X + 2) = 20 and E(X²) = 13. (a) Find E (X) (b) Find V (X)

A: a) We will use the formula E(aX+b)=aE(X)+b E(9X+2)=20E(9X)+E(2)=209E(X)+2=209E(X)=18E(X)=2   Answer:…

Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: 3|n(n+ 1)(n+ 2), Vn E N

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Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the…

A: A detailed solution is given below.

Q: 4 The value of 2 n=1 3n2 will be + 6n .... .

A: See solution below

Q: L(e-3t)= %3D 1 s2- 3 1 .bO s2+3 S-3 1 .dO s +3 1.

A: We can solve it by definition of Laplace method Consider Le-3t = ∫0∞e-ste-3tdt=∫0∞e-(s+3)tdt=…

Q: 14. Find k'(s) if k(s) Ins %3D s2 а. 2s2 b. s4 2 In s C. s3 s3 2 Ins 1 d. s3 s3

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Q: K. 4 12 12 8. 7. Which additional piece of information would prove that A/JK-ALMN? C. NM=15 D. LM=10…

A: The objective is to find out the correct additional piece of information.

Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

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Q: .3 T Evaluate In In e²+j²4

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Q: Seaet =1+ e* + e3x + e(n+1)x enx +esx. n! sx € (0,e*) | ... 2 (п + 1)!"

A: we know that ex=1+x+x22!+x33!+........................+xnn!                      ..1

Q: b) S. 1 /2n+1 n=1 In+1 c) S̟ =E: In° +1 n=1

A: 7) a) The given series to test is S∞=∑n=1∞e-nn. We can use the integral test for checking the…

Q: L{(1+t")e 3t)= (1+)() n! sn+1 -3 1 n! s-3 sn+1 1 n! s+3 (s+3)"+1 n! 1+ sn+1 )() (2) s+3 (1)

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Q: АРТЕ -> Z. K E. P.

A: Given : 2 parallelograms of the same size

Q: Given that n21 and xn = V5n2 + 2n -3n 00 1. Will {xn}, be divergent or convergent? 2. Will E=1Xn be…

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Q: A radioactive sample decays according to the law - -hy where k>0 Suppose c represents the size of…

A: From the given differential equation:   dydt=-ky   So, dy=-kydt...Integrating on both…

Q: 3. The value of c is given by Vn А. /n+1

A: This is a limit problem

Q: If dx is between 3 and 6, then c must be between... O 2/2 and 8. 1 and 6. 1 3 O 2v3 and 3V6. O 3 and…

A: Option A is correct.

Q: If E(0) = 0 then is said to be a(n)

A: if Eθ^=θ then θ^ is said to be unbiased estimate for θ.

Q: 1 (ke)3x For ſ k*e3*dx = + C. If u = 3x, then k =? 3 (1–In 2-1)

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Q: f(n) = n³, g(n) = 6n + 1 е.

A: Given: e) f(n)=n3 and g(n)=6n+1 To find: a and n0 such that a·f(n)≥g(n)

Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent

A: we have to identify the given sequence is convergent or divergent

Q: 14. s(1 + VE)dt +tVE ds = 0; when t = 1,s = 1

A: Firstly , separate the given differential equation and after that integrate both sides.

Q: 2s+2 ds = In\s| – In|s + 2| + C s+3s2+2s

A: Given :       ∫2s+2s3+3s2+2sds=ln s-lns+2+C

Q: 4 The value of 3n2 will be + 6n .... n=1

A: We use partial fraction method to find the required sum of the series.

Q: 1 if Pn (x) dx32 . then n= -1 0.a o none of theseco -1do

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Q: O N (AT) = R(A)-

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Q: k E n(0.1)" Let Sk n=1 Find s3. S3

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Q: n! (j) Sn n'

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Q: Find L{{t"+3)*} O none of the choices given n! sn+1 n! 2. +6 S2n+1 n! 6. sh+1 (2n)! n! s2n+1 +6 sn+1…

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Q: 21x - 42y = 42 176x + ay = 352 What is this exceptional value for a?

A: Given 21x - 42y = 42 176x + ay = 352

Q: In 5 e'dt 2t e 0 V e 2t + 64

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Q: T(n) = 2 * T(n/2) + c, for n > 1 T(1) = a

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Q: 8 4 SS e*dædy O e16 – 1 e16 + 1 *+1 el6 2 O 2e16 – 1 O 2e16 +1 O el6

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Q: 3 n' (iv) En=1 2n³+5

A: (iv). Series  ∑n=1∞n32n3+5 diverges by divergence test for series.

Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: S dt e2t 6-2e²t

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Q: (k) E(-1)"-1. n+1 n=1 Vn +1- Vn – I (1) n=1

A: The given problem is to determine whether the series is converges or diverges using the appropriate…

Q: 1 1 1y 4, then the particular solution is () O0. 01

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Q: m M|L II k=0 CO M« Σ N சிய

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Q: (d) (e) n=1 n=1 3n²+ 1 2n² +3 2¹ (n!)² n2(2n!)

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Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

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Q: 47. Let the assumed particular solution for the given DE be yp = (Ar + Bx² + Cx)e + E. What is the…

A:

Q: 2+4+... +n lim 7n2 + yn

A: limn→∞2+4+....+n7n2+n

Q: 7. E(-1)"- Vn +1 n=1

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Q: 2s+2 ds = In|s| – In\s + 2| + C %3D s3 +3s2+2s

A: Here, we are solving only 1st question and for the remaining question post the question again.…

Q: 2. Find the general solution o- = y(1+e³) 1 له 342433434 11 11 1 "싫

A:

Q: b) Find L[e* S (-os22) dt] and -1 4s+5 * ls-1) (s+2).

A: Laplace transferom and inverse Laplace transferom, using all the properties.