Limits And Continuity Flashcards
Discontinuous functions
Where the value of a function jumps to another value.
Continuous Function
If you can trace the entire graph with your finger without lifting up from the paper.
Point Discontinuity
A single point in time where it’s not on the continuous function.
Jump discontinuities
The function jumps to a new value and stay there.
Intermediate Value Theorem
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.
Addition Property
Equations added together in a limit can split into two separate limits.
Product Property
If two functions multiplied together in a limit can be broken up
Right Hand Limit
Left hand Limit
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-
Finding horizontal asymptotes of ratiaonl functions limits that go to infinity.
Find the highest degree term on the bottom and divide each term of the numerator and denominator by that x^n.
Squeeze Theorem
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.
Continuous function at x=c
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.
If f adn g are continuous at x=c then teh following are also continuous
F+g
F-g
Fg
F/g
If limx->c (g)x=b and if f is continuous at b
the lim x->c f(g(x))=f(b)
List of Indeterminite
Infinity/infinity.
Zero/zero.
Zero*infinity
Zero^zero.
Infinity^zero.
1^infinity
Infinity-infinity.
