2 O Expand Pn = 2x +3x +) in Term of P.f,.

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

A: We have given;

Q: Use the Error Bound to find a valve of N for which Error CSN)<1 x 10-9. is 1.5 3x

A: Error bound for Simpson's rule is defined as follows.  For a function fx, if  f4x≤M, then…

Q: 20. What is the value of the 4th term of the expansion of (y + 2z)°? 16y"z 448y 23 25628

A:

Q: Howin If Z=RCxy) and u=xayg V=x-y show that 3

A:

Q: Find diagonal matriy D is similar with A a A = [3 8-5

A:

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

A:

Q: 2 Evaluate: :S,vte-t² dt.

A: Detailed explanation mentioned below

Q: 4. Prove that for n > 0: E, 2* = 2"+1 – 1. sk3D0

A:

Q: pend. Ex 5) m/MPQ = 10x + 5, m/MPN = 2x, m/NPO = 3(x + 7), and m<OPQ = Find x and m/NPO. Ex 6) m/QPO…

A:

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

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

A: Given integral Apply integration by parts formula to integrate

Q: -3 2. Evaluate: V12-피 + z dar 0,

A:

Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

A:

Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: 00 8tan-in Zn=1 n3D1 1+n2

A:

Q: 6.13 Show that t: = B,/[s//E=, (x;- %3D VI- r in (6.20). |

A:

Q: 8a, 2+ 225n for n> 2 with initial conditions ao 7, a1 83 %3D

A: Given: an=-6an-1-8an-2+225n for n≥2 with initial condition a0=7, a1=83. To find: The solution of the…

Q: (-1)" -Σ S. n=1 Vn+1

A:

Q: (2) O show that you Y2,43, and Yu are solutians to NOTE : Geueral Solufion

A: Thanks for the question :)And your upvote will be really appreciable ;) Solution is provided below,…

Q: X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find…

A: From the given information, X1, .....,Xn~N-3,2 And Zn=1nX1X2+X1X3+...+X1Xn, n≥3 Consider,…

Q: Show that 1/3  Tn +  2/3 Mn  = S 2n

A:

Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

A:

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

A:

Q: 7. (10 pts) Evaluate the integral Sa x4 6x5 - 1dx

A:

Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

A:

Q: Show that 3n2+8nlogn is big-Oh (n²)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 10. Show that S t2 if 0 1, 2(1 - e-) then Ldf %3D

A: Laplace of differential equation.

Q: prove for n=l,2,3. e that +2+3+..+h = ncn+l) 2. %3D %3D

A:

Q: 20 + 7)* Evaluate the integral dæ + 7)* * by making the appropriate substitution: u = dx (2x + 7)4

A: Let's find integration of given function.

Q: 1 Use convolution theorem to evaluate L-1 (s²+9)²)

A:

Q: In ALMN, LN is extended through point N to point 0, mZMNO = (5x – 13)°- mZNLM = (x – 4)°, and m/LMN…

A: Solution-

Q: Suppose m=nd where n is odd and 1<n<m. Prove that 2m+1 is composite.

A:

Q: (3) Let A be m x n (not need to be square). What is the sum of the diagonal elements of ATA in terms…

A: (3) Given that Abe m×n matrix (not need to be square matrix). We have determine the sum of the…

Q: 3. Show that à = (6xy + z³)î + (3x² – z)ĵ + (3xz2 – y)k is irrotational. Find p such that A Vọ.

A:

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: 7. f(t)=3e" cosh (In 21) -2t in two ways.

A:

Q: D. Let Find 2,-

A: We will find out the required value.

Q: a) Expand Ca-b)Catb) b) Hence, expand ox-y+2)(ctytz)

A: a) Expanding (a - b )(a + b)  (a - b)(a + b) =  a(a+b) - b( a+b)                        =  a.a + a.b…

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

A: Given      f(x) = 1512-3x

Q: 4/5elve R(X)= X-2X-5 Using secant e thed, Cerreet apto 2 decimal plases.

A:

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

A: