Question 1184440: Create a function piecewise and verify that the function is uniform throughout the domain and has continuity.
f(x)={g(x), if 0≤x≤a
-----{w(x), if a < x < b
-----{h(x), if b≤x≤c
where w (x) must be equal to one of the following functions:
e^(x^2)
sen(x^2)
cos(x^2)
ln(x^2)
sen(e^x)
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! One such function is  .
This will ensure continuity at the separation points x = a and x = b.
This will also make f(x) continuous over the closed interval [0, c], which by theorem makes it uniformly continuous.
NOTE: As long as the continuity at the separation points are guaranteed, you may use any of the other choice functions,
and the function f(x) will be uniformly continuous over the interval [0,c], by the (Heine-Cantor) theorem.
***By the way, you have a funny way of writing the sine function!
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