2. Prove that |µ(n)| _ S(s) S(2s) n=1 if s > 1.

Q: 1. 4. Use the Min-Max inequality to find upper and lower bounds for dx 1+x2

A: Given integralI=∫0111+x2dxfx=11+x2We can observe that fx is decreasing function .

Q: Suppose X and Y are r.v.s such that E(X) = 4, Var(X) = 48, E(Y ) = 2, andVar(Y ) = 5. Find upper and…

A: To find the upper and lower bounds for E(XY), we need to use the Cauchy-Schwarz inequality. For any…

Q: 9. What is the maximum value of |Log z| |2| 1? on

A:

Q: 9. State and prove the Mean Value Theorem for Definite Integrals by applying the Mean Value Theorem…

A: We have to prove the mean value theorem.

Q: Suppose that |f(r)|I b where and g(r)dx converges. Prove |f(x)dr converges. that

A:

Q: Apply Parseval's identity to the function f (x) = x, - nSxSn and deduce that n16 = 1/12+1/22 + . +…

A: For the solution follow the next steps.

Q: Compute the iteration for the function f(x, y) = 4x³ + 6xy² R=[1,3]x[-2,1]. on the rectangles

A:

Q: If X – 2.58 () < µ < X + 2.58 () - < , given that o = 1.25, determine the error for: n = 15 (ii)…

A:

Q: 17. Use the limit process to fnd the anea of the negion bounded by the graph of f(x)=2x43 ón the…

A:

Q: Suppose that f(x, t) is the probability of getting x successes during a time interval of length t…

A: (a) To show that under the given conditions, f(x, t +t) = f(x, t)[1−α · t]+f(x−1, t)α · t, we can…

Q: 7. Find A. 6 C. 2 fre f(x) dx, given [*[³f(x) + [3f(x) + 4] dx = 18 B. 10 D. 14 3

A:

Q: 31. If f(x)=-1)*(x- 2)* 5* k find: f '(5) = ? k=1 (-1)* 3* a) E 5* k=1 b) (-1)*3* 5* k k=1 (-1)*…

A: Solve the following

Q: 17. Determine k so that d(x) is continuous -x-k, ifx-1 [2x+ 2k, if x = -1 d(x) =

A:

Q: Recall that fn-f in measure if for any e > 0, {\fn(x) = f(x) ≥ €} → 0. - Suppose |fn| ≤ge L¹. Prove…

A:

Q: 8. For x < 1, Σx² = 1/(1-x). (a) Find Σnx” for |x| < 1.

A:

Q: 2. Suppose Y is G-measurable. Prove that Var(Y/G) = 0. %3D

A: Given that Y is G-measurable.

Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: 7. Show that Sx" Inx dx =Inx-+ c. n+1 %3D + C. n+1 n+1]

A: Using integration by parts we can prove the given integral.

Q: 2. 7. S(x³ – 6x + 5)* (x² – 2)dx

A:

Q: .If x is an odd integer, which of the fol- lowing would represent an even inte- ger? (A) x =4 (D) (x…

A: Please refer the attached image for complete solution.

Q: 10. Suppose we have a picker at the front of an aisle of length 20 meters. The picker walks at a…

A: Given f(t)=c 0&lt;t&lt;20

Q: a) I = [ In(1+x²)dx

A:

Q: Compute the exact probability (using integral calculus) that the lecture continues for at least 60…

A:

Q: At time t = 0, then th

A: P(t)=0.5t4-16t3+144t2       , 0≤t≤12At t=0 the sale begins,costco is having a 12 hour sale,The rate…

Q: 6. Let f(x) = 20/(x6 + x4 + x² + 1). %3D (a) Show that for any k e [5,20], there is a point c e…

A:

Q: 2. Given: L//L2, L3//L4 Prove: < 2 E< 4 L2 2. Ls LA

A: Given:- L1 || L2 ,L3||L4        To prove :- ∠2≅∠4

Q: 2. Solve f e** using Simpson's 1/3 Rule with n = 8.

A: The Simpson's 13rule is given below by,  ∫abfxdx=h3fx0+4∑i=1, i is oddn-1fxi+2∑i=2, i is…

Q: Compute [In(4)/3 @3x (@3x + 6)³ dx.

A: To evaluate the given integral

Q: 4. If E(R) exists, show that |E(R)| < E(|R]).

A:

Q: 12. Find the value of k that will ensure that the following function is continuous at x = 3: x² + k…

A: As we know that the function is continuous at x=a if:   limx→a-f(x)=limx→a+f(x)=finite…