Question

1. Which of the following functions (if any) are uniformly continuous on R? a) $x(t) = \sqrt[3]{t^4 + 1}$ b) $x(t) = \sin((t^2 - t + 1)^{-1})$ c) $x(t) = \sin(e^t)$ d) $x(t) = \sin(\ln(|t| + 1)).$

          1. Which of the following functions (if any) are uniformly continuous on R?
a) $x(t) = \sqrt[3]{t^4 + 1}$ 
b) $x(t) = \sin((t^2 - t + 1)^{-1})$ 
c) $x(t) = \sin(e^t)$ 
d) $x(t) = \sin(\ln(|t| + 1)).$

1. Which of the following functions (if any) are uniformly continuous on R?
a) x(t) = √(t^4 + 1)
b) x(t) = sin((t^2 - t + 1)^-1)
c) x(t) = sin(e^t)
d) x(t) = sin(ln(|t| + 1)).

Added by Luis Miguel B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/13/2022

Step 1

A function f(x) is uniformly continuous on R if for every ε > 0, there exists a δ > 0 such that for all x, y in R, |x - y| < δ implies |f(x) - f(y)| < ε. Show more…

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1. In real analysis, or functional analysis, please briefly show your work explicitly and clearly. 1. Which of the following functions (if any) are uniformly continuous on R? a) x(t)= v/t4+1 c) x(t) = sin(et) b) x(t) = sin(t2 -t +1)-1) d) x(t)= sin(ln(|t|+1))