Prove that the function sin(x?) is not uniformly continuous on [0, ). However, it is uniformly continuous on (0, a), where a > 0 is any fixed real number. Suppose f:[0,2n] → R is continuous and f(0) = f(2n). Prove that there exists at least one point c E [0, x] such that f(c) = f(c+x).

Prove that the function sin(x?) is not uniformly continuous on [0, ). However, it is uniformly continuous on (0, a), where a > 0 is any fixed real number. Suppose f:[0,2n] → R is continuous and f(0) = f(2n). Prove that there exists at least one point c E [0, x] such that f(c) = f(c+x).

Name: Answer in detail 4. Prove that the function sin(x²) is not uniformly c
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Answer in detail 4. Prove that the function sin(x²) is not uniformly continuous on [0,0). However, it isuniformly continuous on [0, a], where a > 0 is any fixed real number.Suppose f:[0, 2n] → R is continuous and f(0) = f(2n). Prove that there exists