Please solve using reimanns U(f,p) and L(f,p) notation by implementing the supremum and infimum on the intervals.
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Please solve using reimanns U(f,p) and L(f,p) notation by implementing the supremum and infimum on the...
(5 Marks) ii. Let f:[0, ] → R be the function such that f(0) = cos z for all : € (0,7), and let P be the partition {0, 1} a. Find Ax;, m; and M for all y, where ; represents the number of intervals and my and M, represent the minimum and maximum on each interval. b. Hence find L(P)(Lower sum) and U(P)(Upper sum)
R 1 (1) L + us(t) = u(1) v (0) R2 } v. (!) (t) + 20%*(t) + war(t) = f(t). Let x(t) be volt). (a) Determine iz(t). Hint: Apply Ohm's law on R2. (b) Determine dir()/dt. (c) Determine u(t). (d) Determine vct) using KVL. (e) Determine current through Ry using KCL. (f) Determine vs(t). (g) Determine a and wo.
Usi ng the method of (d) on p. 215, show that f (x) = 2x2 is integrable on to, is and soflolda = 3 that 3 and (d) Consider the function f(x) = x, x € (0,1). For n E N, let P, be the partition {0,1...,1}. Since ſ is increasing on [0, 1], its infimum and supremum on each interval ( 4.4) are attained at the left and right endpoint respectively. with m; = (i - 1) /nº and...
5. Let f : [a, b] → R be bounded, a : [a, b] → R monotonically increasing, and P a partition of [a, b]. (a) Define upper and lower Riemann-Stieltjes sums of f with respect to P and a. (b) Let P' be the partition obtained from P by inserting one additional point x' into the subinterval (2k-1, xk] of P. Prove that for the lower and upper Riemann- Stieltjes sums of f we have L(P, f, a) <L(P',...
please make diagram and show how to solve please y u ), ,, u VIN anu 1 , U), (1, 1) BIR. 27, Let T be a linear operator on Rể that maps (2, 1) onto (5,2) and (1, 2) onto (7,10). Determine the matrix of T with respect to the bases A = B = {(3, 3), (1, -1)).
5 (10 pts) Let b 0 be a number and f)for (o.b, Lt artition of [O, b, wherefor0, 1,2, ns bea 72 ( 1) Find the upper sum U(f, P) . (2) Find lim Uf. P). 5 (10 pts) Let b 0 be a number and f)for (o.b, Lt artition of [O, b, wherefor0, 1,2, ns bea 72 ( 1) Find the upper sum U(f, P) . (2) Find lim Uf. P).
7.3.1 Let U be a finite-dimensional vector space over a field F and T є L(U). Assume that λ0 E F is an eigenvalue of T and consider the eigenspace Eo N(T-/) associated with o. Let. uk] be a basis of Evo and extend it to obtain a basis of U, say B = {"l, . . . , uk, ul, . . . ,叨. Show that, using the matrix representation of T with respect to the basis B, the...
please explain steps. I know U(f,P)-L(f,P)= something that *16. Let S = {S1, S2, ..., Sk} be a finite subset of [a,b]. Suppose that f is a bounded function on [a, b] such that f(x) = 0 if x € S. Show that f is integrable and that sa f = 0.
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F) 3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
Let f(x)-12.2-2x-11 and a(z) = x2 + 12n, where Ir] is the largest integer less than or equal to r. (a) Evaluate the upper and lower sums U(f, P) and L(f, P) of f with respect to or if P is the partition {0、름, î,3.3.2) of [O, 2]. 4 42 (b) Explain why f є [0,2] and use results in part (a) to give a range of fda. Let f(x)-12.2-2x-11 and a(z) = x2 + 12n, where Ir] is the...