7. Modify B(3) to construct a C* function C(2) which satisfies C(2) = 0 if z S 0.. a. b. C(z) = 1 if z 2 1. c. C'(=) > 0 if 0< z < 1.

Q: Mathematicians B. Constante and M. Sosa are having an argument. Professor Sosa claims that it is…

A: Professor Constante is correct.

Q: Let ø : R³ → R be a C² function that is zero for all x € R³ with |x| > R for some big R. Then show…

A: As per the question we have to derive a defination of the Dirac-Delta function. And then using it's…

Q: 5. In which annular domain is f(z) = (a) A(0,0,4) (b) A(0,0,2√2) (a) (b) 1 24 - 16 (d) holomorphic?…

A:

Q: 19. The interval for function |(3 )/2 z-1|<2 is -2/3 ,21 (- 2/3 ,2) (-2/3 ,2] - 2/3 ,2)

A:

Q: The Domain of ƒ(x) = V1- x is

A:

Q: Autocorrelation function is maximum at the origin, i.e., |Rxx (7) |S Rxx (0) XX

A:

Q: 12. Show that the equations p² +q? =1 and (p² +q³)x= pz are compatible and hence find its solution.

A: The equation are, p2+q2=1    ⋯1 And p2+q2x=pz                    ⋯2 To show that these equations are…

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: 5. The function f(x) is defined as: 4x3 +17x2 + 13x +36 x -4 ontinuous for all values of x. What…

A: solution:-f(x)=4x3+17x2+13x+36x+4     x&lt;-45x2+2x+a                       x≥-4f(x) is continuous…

Q: srit ni bomoheq (2)noitsmotan611 betsoibni sdt 1911s riqsig sdt to noitsupe arit 91W (S noitanut…

A:

Q: 4. (a) Let f: X→Y, g: Y→ Z, and h: Y→ Z be functions. Prove or disprove: If gof=hof, then g = h. (b)…

A:

Q: Suppose f(x) is a function with the following properties: · ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, › ƒ"(x) > 0…

A:

Q: 6. Let f(x) be defined as follows: f(x) = {2f x is an integer (1 if x is not an integer Find each of…

A:

Q: Let f: R* N+ with f(x) = [x²1; that is, f(x) returns the square of x rounded up. Characterize f in…

A: Let the function f:ℝ+→ℕ+ be defined by fx=x2. Check whether the function is injective, surjective or…

Q: 6. For each of the following, is it a well-defined function? Explain. (a) (b) (d) a: R→Z a(x) = B(n)…

A:

Q: 11. Let f(x) be any function with the domain (-o, 0). a) Let e(x) = @)+f(-x), Verify that e(r) is an…

A:

Q: Oind Let g(2) = u(2)+iv(2) be ol complete function hiC →C, h(2) = e¯( v(a)+iu(2). Show that if h is…

A: gz=uz+ivz is a complete function and h:ℂ→ℂ by hz=e-ziuz+vz is a entire functionTo prove: g is a…

Q: 15. The number of points where f(x) = |x|² - 3|x|+2 | is not differentiable is/are (C) 4 (D) 1 (A) 5…

A:

Q: 6. Determine all functions f analytic in |2|< 1 and satisfying ƒ(²-) = k+k² 1+k2' k = 2,3,4,...

A: We have to determine all the analytic functions f  in  z&lt;1  such that  f1k = k+k21+k2 ,  k = 2,…

Q: 1. Let f(x) = 12 + 22 + 32 + .+x². Show f(x) is 0(x³).

A:

Q: 13. Let f(z) = z* - a* where f (z) e ¢. Factorize f(z) completely.

A:

Q: If (2 e)(1-3e-38) f(t) = C-¹ · L-₁ { (2²-0") (1 3e-1)} is continuous for t≥ 0, find f(1), f(2), and…

A:

Q: mplete the following statements. x) is positive when g'(x) is decreasing x) is negative when…

A:

Q: 4. a) Suppose that for some specific problem, heuristic function h is admissible. Is h? admissible?…

A:

Q: 11. (2.3.34) Let f: BC and g: A B be functions. (a) Prove or disprove the following statement: If…

A: let f:B→C and g:A→B be functions. (a) prove or disprove the following statement. if f∘g:A→C is an…

Q: 6. Let f(x) = V2x + 1, find as Ax - Ax

A:

Q: Let f(x) = ²-7x-18 ✩ if x = -2 if x=-2 Is f continuous at x = -2?

A: A function is said to be continuous at x=a if limx→a-f(x)=limx→a+f(x)=f(a)…

Q: - g(x) = \x – 9 – x, evaluate at x = 10, 9, 11, and 12 %3D

A: Given g(x)=√(x-9) - x  And we have to evaluate g(x) at x=10,9,11,12