Limits And Continuity Flashcards

1
Q

Discontinuous functions

A

Where the value of a function jumps to another value.

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2
Q

Continuous Function

A

If you can trace the entire graph with your finger without lifting up from the paper.

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3
Q

Point Discontinuity

A

A single point in time where it’s not on the continuous function.

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4
Q

Jump discontinuities

A

The function jumps to a new value and stay there.

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5
Q

Intermediate Value Theorem

A

Given a function f(x) continuous over the interval a to b, and your trying to find the value of f(x) between f(a) and f(b), then there’s at least one solution, x between a and b.

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6
Q

Addition Property

A

Equations added together in a limit can split into two separate limits.

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7
Q

Product Property

A

If two functions multiplied together in a limit can be broken up

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8
Q

Right Hand Limit
Left hand Limit

A

Approaching teh limit from the right hand side and moving left. This is when x->a+.

left hand limit. Approaching limit from the left hand side moving from the right. X_>a-

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9
Q

Finding horizontal asymptotes of ratiaonl functions limits that go to infinity.

A

Find the highest degree term on the bottom and divide each term of the numerator and denominator by that x^n.

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10
Q

Squeeze Theorem

A

If f(x)<_g(x)<_h(x) and the limitsx->af(x)=limitx->ah(x) then limit of g(x) at that same point will be the same.

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11
Q

Continuous function at x=c

A

3 conditions need to be true.
F(c) exists
Limx->c f(x) exists.
Lim x->c f(x)=f(c)

If f is discontinuous at x=c but the limx->c f(x) exists, then we say that f has a removable discontinuity.

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12
Q

If f adn g are continuous at x=c then teh following are also continuous

A

F+g
F-g
Fg
F/g

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13
Q

If limx->c (g)x=b and if f is continuous at b

A

the lim x->c f(g(x))=f(b)

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14
Q

List of Indeterminite

A

Infinity/infinity.
Zero/zero.
Zero*infinity
Zero^zero.
Infinity^zero.
1^infinity
Infinity-infinity.

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