Do no 2 for me and please use the definition of metric spaces 1. Show (in terms of e - 5) that a function f : R → R defined byS(x, y, z) = (2x + 3y + 4z) is uniformly continuous.æ sin (), if (x, y) # (0, 0)2. Determine if a function f : R? →Rdefined by f (x, y) =0,if (x, y) = (0,0)is continuous at (0, 0).3. Show that X = [0,1) with the discrete metric is bounded but not totally bounded.4. Let f : DCR → R be uniformly continuous and {",} be a Cauchy sequence in D.Then show that {f(xn)} is also Cauchy.

Answered: Image /qna-images/answer/14bd7549-c20a-4e34-bc9b-088e0fd4c7af.jpg

Answered: z sin (), if (2, y) # (0, 0) 2.…

z sin (), if (2, y) # (0, 0) 2. Determine if a function f : R2 → R defined by f (x, y) = %3D 0, if (r, y) = (0,0) %3D is continuous at (0,0).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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Do no 2 for me and please use the definition of metric spaces

1. Show (in terms of e - 5) that a function f : R → R defined by
S(x, y, z) = (2x + 3y + 4z) is uniformly continuous.
æ sin (), if (x, y) # (0, 0)
2. Determine if a function f : R? →Rdefined by f (x, y) =
0,
if (x, y) = (0,0)
is continuous at (0, 0).
3. Show that X = [0,1) with the discrete metric is bounded but not totally bounded.
4. Let f : DCR → R be uniformly continuous and {",} be a Cauchy sequence in D.
Then show that {f(xn)} is also Cauchy.

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