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!

## Answer This Question

## Related Questions

- Calculus - Find the horizontal asymptote of f(x)=e^x - x lim x->infinity (e^x...
- Calculus - OK trying again. For what (numerical) of the constant "c" is the ...
- Algebra - What is the answer? I came up with C. is this correct? Thanks for the ...
- Calculus - Sketch the graph of the function that has the following properties. f...
- MATH - I have been trying to do this problem for a couple of days but i cant ...
- Math - f(x)=root sign, and inside that x-2 and g(x)x-7. Which of the following ...
- Algebra - f(x)=root sign, and inside that x-2 and g(x)x-7. Which of the ...
- Calculus-Help Please - Find a function f(x), perhaps a piecewise function that ...
- calculus - State which of the conditions are applicable to the graph of y = f(x...
- Algebra - I know what the answer is just not how to exopress it. Can someone ...

More Related Questions