<p>As you can probably tell, I've forgotten a lot about limits, so here's the question!</p>
<p>g(t) =</p>
<p>t-1 if t < 0</p>
<p>3 if t = 0</p>
<p>t^2 if t > 0</p>
<p>Find each limit if it exists (If it does not exist, give a reason.)</p>
<p>a) lim g(t)
t --> 0^+ </p>
<p>b) lim g(t)
t --> 0^- </p>
<p>c) lim g(t)
t --> 0 </p>
<p>Any help would be greatly appreciated! If I'm not clear about any part of this, feel free to ask, but I hope it makes sense the way I formatted it.</p>
<p>a) 0 (plug in 0 for t^2 because it defines t as greater than 0...so to approach zero from the right you need to use this "piece" of the piece-wise function)</p>
<p>b) -1 (plug in 0 for t-1 because it defines t as less than 0...so the only way to approach zero from the left is by using this "piece")</p>
<p>c) DNE (lim x --> 0+ does not equal to lim x --> 0-)</p>
<p>Thanks.</p>
<p>By the way, is the "g(t)=3 if t=0" only a piece to throw me off and has no relevance when answering the limit problems?</p>
<p>Yes...you would only put 3 down as an answer if the question asked: What is g(0)?</p>
<p>the limit does not exist at t=0</p>
<p>you say the limit exists when lim(t->0+)=lim(t->0-)
ie, left hand limit equals right hand limit.</p>
<p>also, when the function is defined at t,
you need lhl=rhl=g(t)</p>
<p>so, at t=0, lhl=-1; g(0)=3; and rhl=0
so, the ans to (c) is lim does not exist</p>
<p>and as far as i know (an im reasonably sure), the other 2 answers are the same too. but you need to confirm that...</p>