Question

show e^-x is uniformly continuous on R^1.

Answer 1

do you understnad what continuous means?

Answer 2

uniform continuity is for sequence of functions ... just show that e^(-x) is continuous on R^1.

for show that
\[ \sum_{n=0}^\infty (-1)^n x^n/n!\]
converges uniformly to e^(-x). since each term on LHS are continuous, the e^-x will also be continuous.

Answer 3

*or show that

Answer 4

more can be found here
https://www.youtube.com/watch?v=LiC2VPna7qk
just show that
|e^(-x) - F(x)| < epsilon is independent of x
F(x) is series