<p>k i thought i was ready but i am not
can someone explain me limits on graphs and differentiability??
or suggest a site with good explanations</p>
<p>what i am struggling is to look at graphs and see if a limit, continuity and differentiality exists or not.. (hole, a black dot above a hole)</p>
<p>differentiability implies continuity (Remember Washington DC is true. DC for the order). Continuity does not imply differentiability. OK time to go back to cramming for BC.</p>
<p>Continuous if...
Function exists
Limit exists
Function is the limit value</p>
<p>if theres a hole in the graph... does it mean that it still has a limit?? continuity??</p>
<p>what if thers a hole, but theres a black point above it with a different y value (is it continuous, limit exists?)</p>
<p>if there's a hole in the graph, there is still a limit if both sides of the graph are approaching the hole</p>
<p>im not sure on the second one, but im pretty sure that if there's a hole with a black point above it... it's NOT continuous... not really sure though</p>
<p>for the second question....the graph is not continuous because there is a hole....however the limit does exist from both sides. And since it's not continuous it's not differentiable at that point.</p>
<p>also, if you have a function that's continuous, to test if it's deferentiable, test to see if the derivative is the same at both sides.</p>
<p>Limit exists really just if the right hand and left hand limits are the same. Oh yes, no oscillations</p>
<p>It's deferentiable if it is..</p>
<ol>
<li>continuous</li>
<li>no sharp turns (no corners or cusps)</li>
<li>no verticle asomt</li>
</ol>