If S = 2+5+8+ 11+ 14 + 17+.. + 302, then 100 S-Σα+2 (cr + r=0 where c =

Q: ds if s = Find dt 7t + 3 ds dt II

A: We have given;

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

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Q: L{etsin2t – et cos4t} 1 (s-4) a. (s+4)²+16 (s+4)2+16 (s-4) 1 b. (s-4)2+16 (s-4)2+4 (s-4) 1 С.…

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Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: 0.02x10.05x2 = -0.19 0.03x₁ +0.04x2 = 0.52 ○ X₁ = 5, X2 = 8. O x₁ = 7, 2₂ = 8 O x₁ = 8, 2 = 7 O x1 =…

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Q: 2eln In cos 2t 8 + 2 None of the choices Option 2 2s s2 – 2 s2 – 2 Option 5 Option 3

A: This question is based on Laplace transform.

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: 1. Compute each of the following if you can. (a) S(r* – 7z² + 3z + 5Vī + - 11) dn (b) S2 dz (c)…

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Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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Q: The solution of e² = -2 for n = 0,±1,±2,. is %3D ... Select one: O a. In2 + in(1+n) O b. In2 +…

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Q: 1. Given s=6x720: Find a) whure y is at eauilibriuma is increosing <) whe y is docieosing 5) where

A: Given y'=6x2+7x-20 So, equilibrium of y will exist where y'=0…

Q: 1. S(Vz5 + Vx ) de с 6 x2/7 +- 2. x5/6 +x³ +C 1 x3 + C 1 7/2 x3 + C х6/5 + - х3 + C + - O A О в O c…

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Q: 2. sin anod 2 -1)+2) u 2U!S o47 7.

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Q: 1 (2r + 1)(2r + 3) 6 2(2N+ 3) 1 1 Use the method of differences to show that s=1 2N 1 1 Deduce…

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Q: Determine if S3 e S3 is solvable.

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Q: 2 Delermire if fW=x s is even, odd neither.

A: As we know that a function f(x) will be  1. even function if f(x)=f(-x)  2. Odd function if…

Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: X= Sv-6u+sw, y=2u-2v+ 3w and z=8u-bvt 10w implics a (x,y,z)

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Q: The number of the element(s) of order 2 in Z2 O D6

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Q: BELL RINGER 1. V2k2 - 9 - x = 0 If k>0 and x=3 in the equation abové, what is k?

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Q: 1)z = e(4+j3) In(6230") 2) z = (-;)(* 2) z = (-)(r)"

A: (1) The  given complex equation is                                                Z=e4+j3ln6∠30°

Q: (-1)" -Σ S. n=1 Vn+1

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Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

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Q: Ex : Express the Sum o+ 2 +4+6+8 in Sigma nata tion. K = -2 %3D -2

A: First we find nth term of AP then replace k by k+3

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

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Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: 5. 9 ycotx %D CSC

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Q: Suppose, X|0~ Binom(m.0)and e- Beta(a,B), then Var (Y) is equals to, maß

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Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: 5. (BH) Calculate det B, where 0. 4 1 1 В — 1 -2 4 -1 2 1 -1 0 7

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Q: (-1)" S. =È D n=1 Vn +1

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Q: What is the general solution of (* + s) dr + s² (3r + ks ) ds 0 where k is a constat 4rs + r + ks' C…

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Q: 2) Show that L(1-x*)P",)P"mx) dx = 21(1+ 1) Sim 21 +1

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Q: () 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

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: 6) In the process of calculating 7s + a In 7s + b L Where a and b are constant, it is obtained that:…

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Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

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Q: 3) yv1+x²dx + x/1+y?dy = 0 (1+v1+x²)(1+/1+y²) Ans: V1+ x² +/1+ y² In +c (Bali, 2007) xy

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Q: and p(n) iF IF Fon) = 4 sec t dz.

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Q: 6-1718 ss (a) For t= 1.735, should you reject or fail to reject the null hypothesis? prary O A.…

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Q: 3) Ll a, = 5, Qz = 13, end Anta 5 anti - 6 an (n71). Prove by inbuetem that an =2* +3" (n. %3D =

A: The solution is given as

Q: (b) Z/n = (q) if and only if kq 0 for all 1 < k <n.

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Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: Write equation for each ellipse

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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.…