4. Form the inner product < u, Lu > to show that the operator du Lu rE (0, 1) %3D da? Bru = u(0) Bau = u'(1) – au(1) is positive definite (i.e., < u, Lu >> 0) when a < 0. Find the eigenvalues and eigenfunctions of the operator. You do not have to normalize the eigenfunctions. Locate the eigenvalues by graphical solution or sketch, distinguishing (briefly) between the cases a < 1, a = 1, and a > 1. Describe the position in the A-plane of the smallest eigenvalue as a increases from -0o through a = 1 to a = 00.

Q: V(3278)3 + 6230 – 12e90i

A:

Q: . 3류 - 2층 : 3% +4/3) 1

A:

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 3 1/4 + 7 1/8

A:

Q: (5V3)2

A: Explanation of the solution is given below...

Q: 7/2 + 3 4/6

A:

Q: 5/14+1/6

A: 514+16=15+742

Q: 4 11  ✕  5 9

A: Consider the given expression as 411×59. 411×59=4×511×9=2099

Q: 2 3 B={ A= 3 Find: A+B .B+A .A-

A:

Q: 7 11

A:

Q: 9/12+3/24

A:

Q: 5)235

A: Answer : 47

Q: ne binomial:

A:

Q: -3 -10

A: The given equation is:  -3   2÷-10    7

Q: (n + 4)3 =

A: Given query is to expand (n+4)3

Q: V415

A: Given query is to find the square root of 415.

Q: 8 13

A:

Q: 4 10

A: Given: The figure,

Q: Find A3 if A = {1, 2, a, b}

A: Given,      A=1, 2, a, b

Q: 6. Using the data from the contingency table, obtain the value of the test statistic of our test. 7.…

A: Step 1: Given: x1 = number of colored oranges from Skittles brand = 77 x2 = number of colored…

Q: 6 8 27

A: If a line parallel to a side of a triangle intersect the other sides in two distinct points, then…

Q: Find A.

A: Given

Q: 2/5 +7/12

A: Please see the answer below.

Q: Z4×Z6 has an element of order 24. true or false ?

A:

Q: 9. x+8

A: For two intersecting chords , the  multiples of the lengths of the line segments on each chord are…

Q: 3(m – 5) + m

A: 3(m-5)+m=0 3m-15+m=0 add both side 15 we get 2m=15

Q: 8 15 2 15

A: 8/15 -2/15 here simple substraction given and fraction is given  calculation is given inbelow