(vi) P= Q = (P(N); C), and o defined by {1} if 1 € U, {2} if 2 € U and 1 ¢ U, p(U) = otherwise.

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

A:

Q: Solve the following LP problem: max Z 5x, + x, +4x, s/t -, - 5x, + 2x, + 5x, sS 3xL 2. x, + 2x, with…

A: Since the left hand side of the third constraint is not clear, taking it as 1 and solving the LP…

Q: a21 is the susceptible residents becoming infected in day 1 = 0.4 a22 is the residents remaining…

A: Given, In a dormitory there was a common cold epidemic. Each day 40% of the dorm residents became…

Q: 1. Show that, if x(t) and x[n] are even, then x(t) = 2 x(t) dt and > x[n] = x[0] + 2 x[n]. n=-k n=1

A: If a function f(x) is an even function then f(-x)=f(x). Since x(t) , x[n] are even functions…

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

A:

Q: 7. Minimize c = s+ 3t + u subject to 5s - t + v > 1,000 2,000 s + t > 500 s 2 0, t > 0, u > 0, v >…

A: For simplification : s = x1 t = x2 u = x3 v = x4 Let c = Z Z = s + 3t + u = x1 + 3x2 + x3

Q: 2 Exercise.8 Find: P4 (x), Pg(x), L P¾(x) P3(x) dx , LIP,(x)|² dx

A:

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

A:

Q: 6. Prove that for x > -1 then Vn E N, (1 + x)" >1+ nx .

A:

Q: A chemical supply company currently has in stock 100-lb of a certain chemical, which it sells to…

A:

Q: 8. Given that (2x-x*); 0<x<2, S(x) = ; elsewhere. a) Calculate E(X), E(X²) and E 2- X

A:

Q: 4. y= 5e, y-s+ax-3x between x-0 and x=1 about y= -3

A:

Q: 1. re (x, y, z) x). Ly). (z}} - *(*. y, z) . (x)S(x), ly), (z]} (x)E (x, y, z}

A: If x is element then it belong to set And {x} it will be subset of set

Q: 4x obtain the section of the equation Ex xl with the condition u oon X4

A: Let us consider the given PDE is P(x,y,u)ux+Q(x,y,u)uy=R(x,y,u) The equation is solved as Determine…

Q: Exercise 2: Solve the following S-L problem y" (x) + Xy(x) = 0, y(-L) = 0, y(L) = 0. Where L is some…

A:

Q: ー28- Sa Oclumina f dz sabishy cauchy- Reimon quakir f andlgove @ frz= J-2xy ti C-Xyz] +z* @ f(2)=…

A:

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: A certain brand of upright freezer is available in three different rated capacities: 16ft3, 18 ft3,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: Use the theorem of Leibniz in the following problems: If y=x³e2x find y(m) and hence y(3). julm) =…

A: Leibniz rule states that (f(x)⋅g(x))n=∑r=0n Cr nf(n−r)(x)⋅gr(x) Let fx=e2x and gx=x3

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: oo gi ven Y1) =0 , when x=1 > Y=0 In (ito) So 4 Then Putting C= -Ź in li) Inlity?) = Inci+y?) 4 In (…

A:

Q: Suppose that the rate of return for a particular stock during the past two years was 10% and 20%.…

A: The rate of return for a stock during the past two years was 10% and 20%. We want to compute the…

Q: Consider the following LP Min z = 3x, + 2.x, +7x, s.t - x, + X, =10 -2x, + x, - x, <-10 *,X,,x, 2 0…

A: Hi! As per norms, we will be answering the first question. If you need an answer to others then…

Q: 28. (a) Prove that for x e R" and s < t, Ds(x) C D;(x).

A: The notation Dsx represent  an open ball of radius s, centered at x∈ℝn. Let x=x1, x2, …, xn,…

Q: If Saz dy = In|ly +1- Inly +2| + c, then S- %3D y2+3y+2 dt = e2t +3et+2 In(e' + 1) + In(e + 2) + c…

A: The objective is to find the correct option

Q: S F(s) %3D (s+5)6

A:

Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

A: A sample statistics t is said to be unbiased estimator of population parameterγ(θ) if expected value…

Q: dT 4 dp 0; pdT T = To when p= Po dp Po e (T-To) O Option 5 L = e- (T-To) Po O Option 2 -0.5 (To-T)…

A:

Q: In x Compute -dx. 3√√/x 9 X 3 A²x²0 nx-x²²+ C A.- In 2/3 2 4 1 B.- - +C X 3 4/3 4 3 C.--(In x)x-4/3…

A:

Q: 2.4.10 Show that det(e4) = etr(A) for all A E Mn(C). D %3D

A: The given problem is to show the given identity. To show: det(eA)=etr(A) for all A belongs to Mn(C).

Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: 4. For a fully discrete whole life insurance of 10,000 on (45): (i) Beth net and gross premiums are…

A: I proceeded to get 78.5221 for the gross premium

Q: 5. Solve the problem kuxx = xt, u(x,0) = 0, u₁(x,0) = e, Utt - kuxx -∞ 0 ∞ < x < ∞ ∞<x<∞ -

A: Given is the pde. The objective is to find the solution. The solution is for this type of pde is…

Q: 10- The general solution for the PDE (2D, +3D, -6)(D, – 3D,=0 is u(x, y) = e"ExG,(3x-2y)+G,(-2x-y),…

A:

Q: x²y' + 2xy = In(x), y(1) = 2 y = In(x) 1 2 + 1. 3 + - y = -In(x) O Option 1 Option 2 1 1 1 1 1 2 y =…

A: We are given first order non homogeneous linear differential equation which we will solve by first…

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…

A:

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

A:

Q: 8) F(s)=³-ks² 2 Ans. f(1) =2(e"-1)-! k

A: Solve the following

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

A:

Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: The critical points of fr(x.y) x +2y-4y subject to the x + y 9 is (0, ±1), (±2,1) (0, ±2), ( ±V3,2)…

A: Given function is fx,y=x2+2y2−4y and x2+y2=9. We have to find the critical point of the function…

Q: 1.1. Show that Y(n) max(Y1, Y2, ..., Yn) is sufficient for 0.

A:

Q: . Consider the following problem max [(1 - s) √kdt s.a. k= s√k k(0) 1, k(10) libre, s(t) = [0, 1],…

A: Given: The problem is max∫0101-skdt. The given constraints are:  k˙=sk, k0=1and st∈0,1 for all…

Q: Find y' if y= In coshv tanh v. y =sech v-2tanh v O None of the above O Option 4 y=tanh'y y'=tanhv –…

A:

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

A:

Q: (5) Based on part (4), the solution of the problem (E) is: a. u(x, t) = v(x, t) + e" – x + 1. b.…

A:

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.