QUESTION 16 Let X={1,2,3,4} and T={0,X,{1,2}, {3,4}}. Let f: (X,T) → (X,T) defined by f(1) =...
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy (1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...
34.3 Let f be defined as follows: f(t) = 0 for t < 0; f(t) = t for 0 <t < 1; f(t) = 4 for t > 1. (a) Determine the function F(x) = $* f(t) dt. (b) Sketch F. Where is F continuous? (c) Where is F differentiable? Calculate F' at the points of differentiability.
Let f(x,y)=x^2*y. Find the directional derivative of f at (1,2) in the direction of (3,4).
1. Let f:R → R be the function defined as: 32 0 if x is rational if x is irrational Prove that lim -70 f(x) = 0. Prove that limc f(x) does not exist for every real number c + 0. 2. Let f:R + R be a continuous function such that f(0) = 0 and f(2) = 0. Prove that there exists a real number c such that f(c+1) = f(c). 3 Let f. (a,b) R be a function...
Example: Let x, y ∈ Rn, where n ∈ N. The line segment joining x to y is the subset {(1 − t)x + ty : 0 ≤ t ≤ 1 } of R n . A subset A of Rn, where n ∈ N, is called convex if it contains the line segment joining any two of its points. It is easy to check that any convex set is path-connected. (a) Let f : X → Y be an...
(1,3), с %3D (2,1), d (3,4) (1,2), b (4,2), f (5,3) and (5,5). Let 5. Let a = е 3 - {a, b, c, d, e, f, g} be the set of these 7 points. We define the following partial order on S: We have (r, y)(', y) iff x< x and y < / Draw the Hasse diagram of S S 6. We consider the same partial order as in Problem 5, but it is now defined on R2....
3. Let (a) Show that F is conservative in R3. (b) Let T denote the triangular path with vertices (1,1,1), (2,1,1) and (3,2,2), traversed from ,1) to (2,1,1) to (3,2,2) to (1,1,1). Evaluate F.dr Justify your answer (c) Find a function p: R3R such that F Vp. (d) Evaluate dr, where Г is the path y-12, z-0, from (0,0,0) to (2,4,0) followed by the line seqment from (2, 4,0 to 1, 1,2) 3. Let (a) Show that F is conservative...
I need help on this question Thanks 1. Let g(x) = x2 and h(x, y, z) =x+ y + z, and let f(x, y) be the function defined from g and f by primitive recursion. Compute the values f(1, 0), f(1, 1), f(1, 2) and f(5, 0). f(5, ). f(5, 2) 1. Let g(x) = x2 and h(x, y, z) =x+ y + z, and let f(x, y) be the function defined from g and f by primitive recursion. Compute...
#2 #3 #4 #5 please help me with the TRUE or FALSE Given Vf(1,2, 0) = 3i +j -4k, at point (1,2, 0) the directional derivative in the direction <1, 2, -2> is... 5 None of the three. 13 3 13 Considerf (x, y) xe-2* at (x, y) (1,2) Which of the following is FALSE? To estimate f(0.9, 2. 2), let dx = -0. 1 and dy 0.2, calculatedf(1,2), and subtract it from f(1,2). f(1, 2) 1 None of the...
Please solve this problem completely. (1) Length of graphs a) Let a path C be given by the graph of y - g(x), a b, with a piecewise C function g : [a,b] → R. Show that the path integral of a continuous function f : R2 → R over the path C is b) Let g: a bR be a piecewise Cl function. The length of the graph of g on (t, g(t)). Show that [a,b] is defined as...