1.1 Limits Flashcards

1
Q

How do find a limit graphically?

A

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).

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2
Q

What is the difference between f(a) and the limit as x approaches a of f(x)?

A

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.

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3
Q

How do you find a limit using a table?

A

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.

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4
Q

What does it mean for a function to be continuous?

A

You could draw it without picking up your pencil. The limit always equals the function value.

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5
Q

If the limit as x approaches a exists but f(a) DNE, what is going on?

A

There is a removable point discontinuity (hole) at x = a.

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6
Q

If the limit as x approaches a from the left doesn’t match the limit from the right, what is going on?

A

There is a jump in the function at x = a.

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7
Q

If the limit as x approaches a from at least one side approaches infinity what is going on?

A

There is a vertical asymptote at x = a.

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8
Q

How do you tell if a function (usually a piecewise) is continuous at x = a.

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.

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