4. Prove that 3i² + i = n(n+ 1)?

Q: sin(7n) A 1. n2 (-7)" C 2. n=1 (-1)" A 3. 4n + 5 (n + 1)(2² – 1)" - 4. 22n Vn 5. (-1)", n+ 5 C n=1

A: 1. the given series is ∑n=1∞sin7nn2 the given series converges absolutely. therefore, the correct…

Q: Find the general solution to the yiven Euler x* j -3xy = 2.

A: Given differential equation is x^2y" - 3xy' + 9y = 0

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

A:

Q: 3- S e J coscinx) d

A:

Q: дгу ду дх2 5- · + 4y = 0 дх In

A: Given differential equation is y''−5y'+4y=0.....1. We have to find the solution of the expression…

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

A:

Q: Show that x +2 and oe) = *+6

A:

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 5. Use Taylor's theorem to write down an explicit formula for R, (1). Conclude that R, (1) + 0, and…

A:

Q: Solve for z if cosh z = V3i.

A: Simply put cosh z= 1/2(e^z+e^-z)  Then simplify  then finally got quadratic in e^z  then find the…

Q: 3) 12 Glven a = Solve for Vo-

A: Given a=vf-votWe now solve for vo

Q: 2. TER-1 to be, Hn E IN 1+r+4---+ 1-r Shoh that

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

A: Given :- The given expansion x2y + 3y-2 in powers of x+1 and y-2.

Q: 2.5 Solve for z if cosh z = V3i.

A:

Q: 15. sin(2t + 글) dt = e2t-3 8. 7 4 7 64e3 7 4

A:

Q: cos(3rk) In k 5k k 1

A:

Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

Q: Knowing that In(1)=0, the correct second order numerical approximation of In(1.5) is ? (Use as much…

A:

Q: d) solve to 1l o wing equan on. the differenti al 2 dy 3y = 3 n2 + 5 %3D

A:

Q: 12. If IN = 2x + 10 and AT = 26, find x. %3D %3D В 丰 N A O 6 O 12 О 10 8. -

A:

Q: 12. Verify by direct substitution that Un(x, y) = sin nx sinh ny is a solution of Uxx + Uyy 0 for…

A:

Q: Show that sin (2n + 1)z 2n +1 { 7/4 */4 0<まく

A: We will use complex analysis to solve the given infinite sum.

Q: 3. Verify that u = e cos x is a solution of + 8² = 0

A:

Q: 2.2 Based on the Fundamental Theorem of Calculus, show in two statements what may be wrong with the…

A: The given equation is: ∫-13 1x2dx

Q: *(+²–1) cos[cosh (In r")]dr 4.

A:

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

A:

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: 28. IfI:zxzr = 0, ris a. positive b. negative с. zero d. impossible to determine from the…

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

Q: Solve for z if cosh z = v3i.

A: Given cosh z=3ι. Expand cosh z to solve for z.             ez+e-z2=3ι              ez+e-z=23ι…

Q: •1-i Evaluate 4z dz . J3i

A:

Q: 2 16n |xV8 - x³ dx: 9/3 3 11) Show that

A: Properties of Beta Function:  β(m, n)=∫01xm-11-xn-1dxβ(m, n)=Γ(m)Γ(n)Γ(m+n) ;       m&gt;0,  n&gt;0…

Q: Evaluate plti 5. S z² dz using the formula [2² dz = A 3

A: This question is related to definite integration, we will solve it using given information.

Q: (x – 2)² – In x = 0, [1,2]

A: The given equation is x-22-ln x=0 the formula for the secant method is given by…

Q: # 2. So sin 32 dz C: Izl=3 (z-5)

A:

Q: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

A:

Q: Find o v' (+2) dt. Show the computations that lead to your answer

A:

Q: 2) × 2+4i 3+1 and 2=3-1 2+i 2 prove that x² + 3xy + y² = 6 if it was

A:

Q: General solution of 3 cot 0 = -V3, where n is an integer

A:

Q: 4. Use the first Fundamental Theorem of Calculus to find 3r 2-1 dt 12 +1 sin 2z

A: Fundamental theorem of calculus Let us consider the continuous function f(x)  on the interval [a,b]…

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: 13. a) Show that EX=o (-1)*(")=0, and then verify that ) +C) + C) + - - G) +G) + () +- ... = b)…

A: We will use of binomial theorem to solve it

Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt