please answer question 4 part b xs there s m 4. Show in each case that...
b) i. Using e-8 definition show that f is continuous at (0,0), where f(x,y) = {aš sin () + yś sin () if xy + 0 242ADES if xy = 0 ii. Prove that every linear transformation T:R" - R" is continuous on R". iii. Let f:R" → R and a ER" Define Dis (a), the i-th partial derivative of f at a, 1 sisn. Determine whether the partial derivatives of f exist at (0,0) for the following function. In...
please answer to all parts
4. In each case, determine whether W is a subspace of the F-vector space V. (a) F=Q, V =R2, and W = Z?. (b) F=R, V = RP, and W = {(x,y) ER?:zy >0}. (c) F=R, V = R', and W = {(x,y,z) € R3: x > 0, y > 0, 2 >0}. (d) F=R, V = C, and W = {(x, y, z) ECS:x + 2y + iz=0}. (e) F = Q, V =...
u=2i-j+k v = 37 - 4k w = -51 +7 QUESTION 1)Find the volume of the parallel face determined by the vectors QUESTION 2) f(x, y, z) = xy + y2 + zx a) Find the gradient vector of function f b) Calculate the gradient vector at point P (1, -1, 2) of function f. c) Direction in the direction of the vector v = 3i + 6j - 2k at point P (1,-1,2) of the function f find the...
Please answer a,b and d(most important) . TQ
(BEKG 2443) PART B: ANSWER ONE QUESTION ONLY QUESTION 4 Given S is a surface for a part of the sphere x2 + y2 + x2 = 4 that lies above the cone z = √ x² + y² (a) Find a parametric representation for the surface S in terms of 6 and 0. Then, determine the domain of O and e. (5 marks) (b) Based on the expression written in (a),...
Question 4. For S: B(ro, 0), assume that f: S R" is a function such that f(x) f(y)Plx - y f(0) c and for some pi1 a. Prove that for any x E S f(x) elpilx|< \cl + Pi*o b. Prove that there exists some rı > 0 such that c|< r1 implies f(x) e S for all x E S (Find a particular choice of ri that will work.)
Question 4. For S: B(ro, 0), assume that f: S...
Question 13 4 pts Solve the problem. Find F '(x) if Flx)= dt Question 14 4 pts Find the domain and range and describe the level curves for the function f(xy). fix. y)-25-2 O Domain all points in the xy-plane; range real numbers 0szs S; level curves: circles with centers at (0.0) and radi r,0<rs5 Domain all points in the xy-plane satistyingx2 y2s25;range: real numbers 0 szs 5: level curves: circles with centers at (0.0) and radi r. 0crs5 O...
dk how to do question 3 and 4 . help !!
Part 2 nts) 3. Let x = e' cos 0, y = e' sin 0, and suppose f: R2 + R is a C f(e cos 0,e" sin 8). Show that function. Let g(r, 0) = 09 (,0) + 3 (1, 0) = e) (no elle" cos ,esin ) + face" cos 8, e' sine)). nts) 4. Let S = {(x,y) € R2: xy #0}, and define f :...
a. A function f: A B is called injective or one-to-one if whenever f (x) f(u) for some z, y A then y. Which of the following functions are injective? In r-y. That is Vr,y E A f()-f(u) each case explain why or why not i. f:Z Z given by f(z) 3 7 ii. f which maps a QUT student number to the last name of the student with that student number. b. Suppose that we have some finite set...
Can you please answer part a and part b of the question.
3. Statements: Let UC R Definition 0.1 . A function f : U → R is uniformly continuous on U if Ve > 0, 36 > 0 such that y(10,1) E U × U ifla-zal < δ then If(x)-f(zo)I < E (a) Without using negative words, state what it means to say that g(x) = ejs not iniformiy continuous on the interval U = {x R | x...