(7) State whether each of the fOllowing is true or false and justify your answer: (a) {r e Q :0

Q: 49. f(x) = alst %3D n=0 Selet ai 50. f(x) = 2 (-1)+1(x – 5)n n5" n=1 * (- 1)n+1(x – 1)"+1

A: f'(x)=∑n=1∞ (-1)n+1n(x-5)n-1n5n      =∑n=1∞ (-1)n+1(x-5)n-15n Apply the ratio test to check the…

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

A:

Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: Find the solution of the initial value problem: y' (2x - 17)e, y(0) = In(72) = (a) Evaluate y(-1)…

A:

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: 1 z/2 Find ' (x) if k(x) = e Provide your answer below: K(x)=

A:

Q: -2 Let a = 3/2 1 [3/2 -1/2 E GL2(R) -1 1. Compute (ba)-1 2. Solve for x in ax = b

A: Given,            a=-2132-12 , b=-1321-1

Q: Problem B1: Prove that for all x E R sufficiently large, r³ – 7x > 4x2 + 2. -

A: That's easy. Thumb up. Have a good day!!!

Q: 1.2.10 1 if x < a, f (x) = 2a elsewhere on (-T,"|, where 0 < a < T. Sketch for two different choices…

A: Since, you have post multiple question here. I am answering first one. Please post again with…

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

A:

Q: 2.2 Solve y = x – y + 1 for y(0) = 1 and x = 0(0.1)0.3 , using the Runge-Kutta method of order four.…

A:

Q: Quark wants to extract ALL of the consumer surplus by requiring his customers to purchase a minimum…

A:

Q: 4.2 Apply the appropriate method to calculate the following: 1 = f***-8 I = S x2-4

A:

Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

A:

Q: п-1 k n-2 n-1 n-2 () x6n-10 = p %3D k - 4 X6n-9 = 4 n-1 n-1 n-1 k n-1 X6n-8 = h X'6n-7 = P k n-1 n-1…

A:

Q: NO.4 DE. 2.1 In the following problems, eliminate the arbitrary constants by any of the three…

A:

Q: The function h(x) given by h(x) = –6 – 8.2944x - 4/5x + 3.84x³ has a critical number c = = -1.2.

A: We have given function hx=-6-8.2944x-45x5+3.84x3 and critical number c=-1.2

Q: x2n+1 El-1)"; 2n +1 n=0

A:

Q: 1. max z = 2x1 + 3x2 X1 + 2x2 < 10 3x1 + 4x2 S 25 s.t. X1, X2 2 0; x1, X2 integer

A:

Q: For the following conjecture, state the null and alternative hypotheses. The average resting pulse…

A: Given that: Population average=μ=70

Q: 8. Solve the following LP algebraically. a. Max Z= 150X+ 160Y subject to: X+Y 20 Y>15 X, Y>0

A:

Q: 1. Find two positive numbers such that their product is 192 and the sum of the first and thrice the…

A: We have to use the application of derivatives to solve this given problem

Q: 1 0 Problem 4. Let p(x) = 5x? – 3x +2 and suppose that A = 0. for some y E R. Evaluate p(A).

A:

Q: 12. Solve the problem: Utt = c*upx + Ax, 0 0, A= constant, и (х,0) — 0, и (0, t) — 0, Ut (x, 0) =…

A:

Q: Let h(x) = e" + 2x. Use the Intermediate Value Theorem to show that e" + 2x = 0 has at least one…

A: First it is required to show that h(x)=0 has at least one solution, where hx=ex+2x

Q: 3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

A: Now plotting the graph of given function we get :

Q: 6. Find the smallest constantr so that o(x) == x" is a solution to 3z'y" +11lry -3y= 0, for z >0 -3…

A: 6.ϕr=xr is a solution to 3x2y''+11xy'-3y=0, for x&gt;0

Q: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1.…

A: Maclaurain series

Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: •1 1 g(x) = dt 2x In(t + 1)

A:

Q: nine all the critical points fo

A: Given that : The equation of the function is f(t) = t23 ( 2t - 1) .

Q: Question 4. Prove that L°[0, 1] C L°[0, 1). Hint: Hölder's inequality

A:

Q: A useful consequence of Taylor's theorem is that: |æ – c|" max|f(n+1)(2)| (n + 1)! > (æ)"y| (1)…

A:

Q: 1.1 Solve for x in cach of the following: 1.1.1 * +x-12=0 1.1.2 V2x+1 =x-1 1.1.3 2 = 27 1.1.4 x…

A: As per the guidelines we are allowed to solve one question. So please upload the other questions…

Q: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0&lt;λ&lt;x0:…

Q: Find the x values of the two critical points of: 3(x- 1)23 6x – x² - 5 if x > 2. if x < 2 f(x)%3D X…

A: we have the given function is ;  f(x)=3(x-1)2/3if x≤26x-x2-5if x&gt;2

Q: Which of the following initial condition will NOT satisfy y(x) = c(1 – x²)? 1. y(0) = 1 2. y(2) = 1…

A: Let's find.

Q: n In x (e) fn(x) = x > 1

A:

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: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: 21. The equation x - 2·* - 0 has a root in the interval A OS x s1 B ISXS 2 € -1s x < 0 D -2 < x s-1

A: Exponential equation

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: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

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

A:

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

A:

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Find the radius of convergence and interval of convergence of given infinite series.

Q: 3. Consider the following knapsack problem: x1 + 3.x2 + 6x3 + 7x4 max x1 + 2.x2 + 3.x3 + 4x4 < 11…

A:

Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

A:

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: 9. Suppose that N(h) is an approximation to M for every h > 0 and that M = N (h) + K,h+ K,h? + K3h…

A: