how does one determine the continuity of the function (sqrt of t)(1+t)?

Question

anonymous · Answer

$f(t)=(1+t)\sqrt{t}$, like this?

anonymous · Answer

yes

anonymous · Answer

this is a product of 2 functions.  since both are continuous over their domains, their product will also be continuous so long as t stays within the domain of both functions.

the only point that really doesn't have continuity is t = 0.  this is because $\lim_{t \rightarrow 0}(1+t)\sqrt{t}$ DNE (Does Not Exist).  It's a one-sided limit, that is $\lim_{t \rightarrow 0^+}(1+t)\sqrt{t}$ exists and is 0.  therefore f(t) will be continuous for all t>0.

anonymous · Answer

does that make any sense?

anonymous · Answer

you there?

anonymous · Answer

yes. i am thinking about what u said

anonymous · Answer

okay, sorry to disturb

anonymous · Answer

it makes sense. thank u

anonymous · Answer

i'm around helping others but if you have any questions or comments, just post and i'll return to help you

anonymous · Answer

oops, nevermind.  hope i helped.