Suppose xo. X1....., are distinct numbers in the interval [a,b] and f € C**[a,b). Then, for each x in [a, b]. a number 5(x) (generally unknown) between xo. X.....X, and hence in (a,b), exists with flas)(E(x)), (n+ 1)! f(x) = P(x) + *("r - x).. (Ix- x)(r-x)- (3.3) where P(x) is the interpolating polynomial given in Eq. (3.1).

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

A: Professor Constante is correct.

Q: 45. Let g(x) = [x]. Find a) g-¹({0}). c) g-¹({x|0<x< 1}). b) g-¹({-1, 0, 1)).

A:

Q: Let a, b c and d be real numbers. Show that ab-cd = b(a-c)+c(b-d), and deduce that |ab - cd| ≤…

A:

Q: 8. Let X and Y be sets, and let C and D be any two sets of Y, and suppose that F: X →Y is a…

A:

Q: 14. Let X = {n eN:0 < n < 999} be the set of all numbers with three or fewer digits. Define the…

A: A

Q: Let F(x) = f(x) = x" for x = [a, b] and some positive odd integer n. Show [₁ 62_a²n 2 fdF =

A:

Q: 2.22 Let f be continuous at a, and e > 0. Show there exists & > 0 such that I1, 12 E Df n (a -- 8, a…

A:

Q: 5. Find the domain off(z-In(e*-3). Then find f-1 and its domain.

A: f(x) = ln(ex-3)The function "ln" is defined for positive numbers only.Hence, x should be such that…

Q: Let the p.d.f. f(x) be positive on and only on the nonnegative integers .Give that f(x)=4/x f(x-1),…

A: Given that:

Q: Which of the following function is NOT Q, (n)? А. п —333п? nlgn С. п-1gn D. 219 n E. None Е.

A:

Q: Show {5, 10, 15, 20, - - ·} is countable. (Hint: Use the function f(n) and onto). = 5n and show it…

A: 4 Given set is 5,10,15,20,....... We have to show that the set 5,10,15,20,...... is countable. Let a…

Q: 6. Find f'(1) if Ax) = nx

A:

Q: 2.59 Find || f |sup if a) f(x) = x on (-1, ). So if x E Q, b) f(x) = – x² .2 if x ¢ Q. -

A:

Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

A: In this question we can easily observe that that output of the function is the remainder when any…

Q: If ƒ = {(1, − 1), ( – 3, 1), (2, the following values of f and g. a. f(1) b. g(2) = = 3 c. g = d.…

A: Given :- f=1,-1,-3,1,2,14,π,1 and g=2,-1,-3,-2,34,-1 To find:- f1 g2 g34 f2 g-3 fπ

Q: Let f1, f2, .. fn be n real-valued, differentiable functions.- Prove that e :[fif2 ... fn] = (fif2…

A: We have to prove that the given formula.

Q: 1. Suppose f: A B and W and X are subsets of A. (a) Will it always be true that f(W U X) = f(W) U…

A: We are given that f: A --&gt; B and W and X are subsets of A. For (a), The given statement f(W∪X) =…

Q: 2. Rewrite each of the implications below using all 4 forms: (1) only if, (2) is sufficient, (3) is…

A: (a) If a function f is differentiable, then f is continuous.Only if: Only if f is continuous, is f…

Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

A:

Q: 10. |G/H| [G:H]. *True False

A: 10. True or False: |G/H|=[G:H]