1.1 Limits Flashcards
How do find a limit graphically?
Trace your finger along the graph from left and right and see what the y-value gets close to. Where does the road go at a certain x-value? Ignore what is actually happening there (the bridge).
What is the difference between f(a) and the limit as x approaches a of f(x)?
f(a) is what the function actually equals at x=a (the bridge). The limit is what the function is getting close to around x = a.
How do you find a limit using a table?
Plug in numbers close on either side (like .999 and 1.001) and see if the y-values are getting close to one specific number.
What does it mean for a function to be continuous?
You could draw it without picking up your pencil. The limit always equals the function value.
If the limit as x approaches a exists but f(a) DNE, what is going on?
There is a removable point discontinuity (hole) at x = a.
If the limit as x approaches a from the left doesn’t match the limit from the right, what is going on?
There is a jump in the function at x = a.
If the limit as x approaches a from at least one side approaches infinity what is going on?
There is a vertical asymptote at x = a.
How do you tell if a function (usually a piecewise) is continuous at x = a.
3 parts: show that the limit from the left and right match. Show that f(a) also matches. State that f(x) is continuous at a because all three are equal.