3.11. Let z1, 2,, Zn and w1, w2, , Wn be complex numbers. Estab- lish Lagrange's identity 2 ZkWk - zwk|2, |k=1 k=1 k=1 k

Q: 4. The following function is a cubic spline for what values of a, b, c? 2x3 – 3x2 + 3x – 6 for 0 < x…

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Q: Let C be the shortest path that connects a to ni and I = S, (coshz – 1)dz. Then %3D O I=-sinh n+…

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Q: Let C be the shortest path that connects n to ni and I = [, (sinhz + 1)dz. Then O I=-sinh n+ n(i-1)…

A: Second option is correct answer i . e . I = -1-cosh(π)+π(i-1)

Q: Explain step by step how te solve the guestons given below. You mustn't numerical exemples. give…

A: Answer to question 1.   Given the function is y=fx.   Differentiate the function with respect to x.…

Q: dn-1 for all n E Z with n > 2. Prove that for a 2. Let d = 2, and d, neN, d, =. %3D %3D %3D

A: Mathematical Induction is a special way of proving things. It has only 3 steps: Step 1: Show it is…

Q: 5. Triangle JKL with verfices J(1,-1). K(2, 3), and L(3, -2): x=4 J': L': K'

A: In the question it is asked to take a mirror image of triangle ∆JKL about x=4. Coordinates of…

Q: Please help number 38. Do it step by step.

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Q: 1. Compute P(8), and find the exact values of the six circular functions given that e =- 135°. %3D

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Q: (в Suppose m and n are constants and m #n. Evaluate 1 (A) √ [n² m² -cos(m− n)x-- -cos(m+n)x] + C m+n…

A: To solve the given integral.

Q: The equation kk+4 – Yk = (4.71) has the characteristic equation pd – 1 = (r2 + 1)(r² – 1) = (r +…

A: To Determine :- The characteristics equation .

Q: B. Solve the following linear independent and Wronskian. 1. A-- t 3 ine functione 4. Consider the…

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Q: Theorem 13.Let {xn} be a solution of Eq.(1). Then the following statements are true: (i) N>0, the…

A: To get the inequality (48). XN+1≥bdA+B+C+D+bXN−kdXN−k−eXN−1               .......................48…

Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: 2:31 AA A learn-us-east-1-prod-fleet01-xythos.c C Section 3.2 Homework (from the 5" Edition) 1. Let…

A: 1.(i) we have x,y and z ∈R           and R  is a feild with respect to addition and multiplication…

Q: 4. The indicated function yi (E is a colutian of the given equatiom Use differentral the method 01…

A: We will find out the required solution.

Q: O Let n 3 be an integer. How many roots of the equation 2" + 3z +1 = 0 lie in the closed annulus {z…

A: We will use rouche's theorem.

Q: 2 3 2 3 2 3 Let G= S3 and H={(; 3 2 Then the number of disjoint cosets in G/H is H. 6 O 3 2 O

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Q: 20 Use this graph of y = f(x) and the fact that 3 5 6 1 10 il i2 i: -2+ to compute the following: L…

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Q: 21.What are the positive and ngative rcots of square root of 64 a. ±7 22 - 25.Solva for the roots of…

A: root=  a solution to an equation, usually expressed as a number or an algebraic formula.

Q: Question- let G De 4. H and k. then of ZLHS and 2

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Q: Theorem 13.Let {Xn} be a solution of Eq.(1). Then the following statements are true: (1i) b 0, the…

A: To get the inequality (49). XN+1≥bdA+B+C+D+b2d2−be               .......................49 We have…

Q: e) C) modulus of d) Argument of 3+4i K = 0, 1, 2, 3, 4 roots for WK K (5) ½ se i (ton+ (1/3))/5 ws…

A: given z=3+4i and We have to draw the given roots on an Argand diagram

Q: Find an equatlon Of the ine Through G1,2); Perpendicular to me 2x+ 5yt 8=0 line

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Q: 5.19. In this problem f(z) = P and R > 1. Modify our computations in Example 5.14 as follows.…

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Q: A₁ Let 2 + sinh (2²) - ₁₁ = 27 where w = f (x, y, z)- 1 पुर Find aw дх Jw and Iw > zw. ay dz 3/20

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Q: 51. If objects of weights x and wi are suspended from the balance in Figure 14(A), the cross-beam is…

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Q: A bin of 5 transistors is known to contain 2 that are defective. The transistors are to be tested,…

A: Conditional probability Given discrete random variables, X and Y with joint probability mass…

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: The energy stored 'W' in an inductor is given by W (10 * 10-3)te-2dt %3D

A: Given query is to find the value of the integral.

Q: Theorem 6 If (b+ f) > (c+r) and (d + g) > (e + s), then the necessary and sufficient condition for…

A: In the given question we have to determine red, which is let…

Q: Problem 2. Suppose that d is an odd integer. Let f: Z/dZ → Z/dZ_be the function f(n]) = [2n]. Prove…

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Q: 5. (a) Solve the cauchy problem given by x²ux + xyuy + xu = Xx-y where (x, y) + (0,0) if u(x, xln x)…

A: Given x2ux+xyuy+xu=x-y where x,y≠0,0 if ux,xlnx=-lnx, x&gt;0

Q: Let z=3+7i and w=7−8i . Find out the following in the x+iy form.

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Q: -4z2-4 Let C: |z-1|=3 and I = Pc 7?-1 dz. Then O I=2ni O I=4rti |=0 (without applying Cauchy-…

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Q: Ar, So, and ka are the Tano constants and have no significance at all beyond allowing me to insert…

A: Consider the given equation: To apply finite difference.

Q: = z and suppose, corresponding to z = 1, we have w = 1. (a) If we start at z = 1 in the z-plane and…

A: Given that: w2=z where z=1 and w=1 In the plane basically there are three axes that are co-ordinated…

Q: to 2. to' to 16? 0.1 1. 1o Gisaph of lo0 4= on Slog-log axes with boints (,1),(2,2),(3,3),(4,4),…

A: To determine: Graph of y=x on log-log axes with points (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) (10,10)…

Q: 12 10 8- 6- raph k(x) = x| at right. The graph of 3 23456 789 10 1I 12-11-10-9-8-7-6-5-4-3-2 %3D (x)…

A: Given:

Q: 13.5.3 Write a in the form a = a-T+aNN at the given value of t without finding T and N. r(t) = (t+…

A: To write a in form of a=aTT+anN  given r(t)=(t+5)i+(-2t)j+t²k, t=-1

Q: 1. Let x (x,) E l. Find x if 11-- a. x = 2 %3D

A: This is a question of functional analysis in lp space.

Q: Let z = -1 - i and w = -2 +i. Evaluate z * w. a. 4V2 25л (25m cos 3 +i sin Z * w = 12 12 Ob. 4/2 z *…

A: Given z=-1-i and w=-2+23i

Q: Let C be the shortest path that connects a to ni and I = ſ, (sinhz + 1)dz. Then |=-1-cosh n+ n(i-1)…

A: First option is correct.

Q: Theorem 6 If (b+ f) > (c+r) and (d+ g) > (e + s), then the necessary and sufficient condition for…

A: Given equation is  xn+1=axn+bxn-1+cxn-2+fxn-3+rxn-4dxn-1+exn-2+gxn-3+sxn-4             (i) It is…

Q: Let C be the shortest path that connects n to ni and I = S. (sinhz + 1)dz. Then O I=-sinh n+ Ti(i-1)…

A: Option C true.

Q: 4. Match each graph with its equation. (x – 2)² a. y = - (x-1)² x - 2 2. b. Y = x – 1 1. I – 2 54-3…

A: y=(x-2)2(x-1)2  1st option is correct answer.

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(1, 9) what is the y coordinate of R?

A: