Answer to Question #103884 in Calculus for BIVEK SAH

Question

Check whether the function, ,f defined below, is uniformly continuous or not:

f(x)=x^(1/2), x∈[1,2]

Answer 1

$f(x)=\sqrt {x}\ , \ \ \ x\epsilon$ $[1,2]$

This function is valid for positive x and in the domain [1,2] the entity inside the square root function is positive so this function is continuous over the domain [1,2]

It can be also checked using graph

so from the graph we can see that the function is continuous for x>0

For function to be uniform continuous then the function must satisfy the two condition :

1) function is continuous in [a,b] and interval is closed

2) limit at x=a and x=b is finite

so the above two conditions are fulfilled hence the function is uniformly continuous