Proof this and write clearly, thanks
![Let f : Rk → Rm be a continuous map and C be a C1 curve in Rk. Then 1. if k- 1 and C- [a,b], then ofdsl-1(dts le Ifids Jea f(](http://img.homeworklib.com/images/d2be415b-6b7b-4bc1-b226-a15362dadc82.png?x-oss-process=image/resize,w_560)

Let f : Rk → Rm be a continuous map and C be a C1 curve in Rk. Then 1. if k- 1 and C- [a,b], then...
Please answer both part. Thanks.
In the power method, let rk d(x(k+1))/ф(z(k)). We know that limk-oo rk Show that the relative errors obey 1- Ai where the numbers ck form a convergent (and hence bounded) sequence. (Continuation) Show that rk +1-λι-(c+&J(rk-A) where Icl < 1 and limn-o0 Sk 0, so that Aitken acceleration is applicable.
In the power method, let rk d(x(k+1))/ф(z(k)). We know that limk-oo rk Show that the relative errors obey 1- Ai where the numbers ck form...
3. Let t be the co-ordinate on A (C) and let z, y be the co-ordinates on A2(C). Let f 4z? + 6xy + x-2y® E C[x, y] and let C be the curve C-V((f)) C A2(C) (You may assume without proof that f is an irreducible polynomial, therefore C is irreducible and I(C)- (f).) (a) Show that yo(t) = (2t3, 2t2 + t) defines a morphism p : A1 (C) → C. [3 marks] (b) Show that (z. У)...
Suppose f(x,y) is such that V f is continuous everywhere. Let C be the smooth curve given by F(t) = (cos(t), cos(t) sin(t)) for 0 <t< 7/4. Suppose we know that f(0, 1) = 3, $(1,0) = 7, f (VE) = 2, 2' 2 Use this information to find Sc Vf. dr. Show all work and expain your reasoning.
Problem 5 Let f : [0,1] → R be continuous and assume f(zje (0, 1) for all x E (0,1). Let n E N with n 22. Show that there is eractly one solution in (0,1) for the equation 7L IC nx+f" (t) dt-n-f(t) dt.
l maps is a quotient map. 4, Let ( X,T ) be a topological space, let Y be a nonempty set, let f be a function that maps X onto Y, let U be the quotient topology on induced by f, and let (Z, V) be a topological space. Prove that a function g:Y Z is continuous if and only if go f XZ is continuous.
l maps is a quotient map. 4, Let ( X,T ) be a topological...
Let C1 be the semicircle given
by z = 0,y ≥ 0,x2 + y2 = 1 and C2 the semicircle given by y = 0,z ≥
0,x2 +z2 = 1. Let C be the closed curve formed by C1 and C2. Let F
= hy + 2y2,2x + 4xy + 6z2,3x + eyi. a) Draw the curve C. Choose an
orientation of C and mark it clearly on the picture. b) Use
Stokes’s theorem to compute the line integral ZC...
Let R be the region shown above bounded by the curve C = C1[C2.
C1 is a semicircle with center
at the origin O and radius 9
5 . C2 is part of an ellipse with center at (4; 0), horizontal
semi-axis
a = 5 and vertical semi-axis b = 3.
Thanks a lot for your help:)
1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
JO # 2. Let the linear operator K : C([0, 1]) + C([0, 1]) be defined for each continuous real valued function f on [0, 1] by (Kf)(x) = 1 | tf(t) dt. a. Find a range of values for the parameter 1 for which the operator norm of K is strictly less than 1 with respect to the norm on C([0, 1]) given by Il gl. = sup{lg(t)| :te [0, 1]}. b. Describe an iterative process for solving (generating...
Let
fx=x2-x-2(x2-4)
if
x≠±2c
if x=2
Find c that would make f
continuous at 1. For such c, prove that f is continuous at
1 using an ε-δ proof.
x2-x-2 с 1. (10 marks) Let f(x) = (x2-4) if x # +2 if x = 2 Find c that would make f continuous at 1. For such c, prove that f is continuous at I using an E-8 proof.
mk-G) ( m+1 ). 2. let 1 k m and let f : Iml+ Ikl be a surjective map. Show that ΣmifO
mk-G) ( m+1 ). 2. let 1 k m and let f : Iml+ Ikl be a surjective map. Show that ΣmifO