Posted by Amy on Tuesday, June 16, 2009 at 8:10pm.
Show that f is continuous on (infinity, infinity).
f(x) = x^2 if x<1 and the square root of x if x is greater than or equal to 1.
I'm not entirely sure how to start this. Help is greatly appreciated :)

Calculus  drwls, Tuesday, June 16, 2009 at 9:21pm
f(1) = 1
For x<1, the function approaches 1 as x>1 from below.
Therefore the function is continuous at x=1. It is also defined and continuous for x>1 and x<1.
Therefore it is continuous on (infinity, infinity)

Calculus  Amy, Tuesday, June 16, 2009 at 10:06pm
Many thanks!
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