Continuity?

Question

Given f(x) =
{(c^2-x^2), if x<0
{(c cosx), if x>0

what is c so f(x) is continuous

I think i have the answer but i need to be sure.

Thank you :)

Answer 1

When x --> o from the left, the limit of f(x) is c^2 - 0^2 = c^2.
When x --> 0 from the right, the limit of f(x) is c*cos(0) = c.
Since f(x) iff f(0) is defined and the left limit when x --> 0 equals the right limit when x --> 0, we must have that:
c = c^2 ==> either c = 0 or c = 1.
Regards
Tonio

Answer 2

c=0.

The left hand limit as x --> 0 is 0^2 - x^2 =zero

and

the right hand limit as x --> 0 is 0cosx = zero.