a horizontal line in which the limit approaches but never touches as the limit of the function approaches positive or negative infinity.
What is a horizontal asymptote?
100
implies f is increasing
What is f'>0?
100
gives speed and direction
What is velocity?
100
to determine concavity, the _______ _________ must change sign from positive to negative or negative to positive
What is the second derivative?
100
NET change = NET area
What is an integral?
200
the vertical line that a graph approaches but does not cross or touch in which the limit equals positive or negative when x is aproaching "a" from the left and the right
What is a vertical asymptote?
200
implies f is decreasing
What is f'<0?
200
=absolute value of velocity
What is speed?
200
When a graph is increasing and concave up
What is f(x) increasing at an increasing rate?
200
Total Change=Total area
What is an integral of absolute value?
300
When the limit of from the right equals the limit from the left
What is the exsistence of a limit?
300
implies f is concave up
What is f">0?
300
when velocity and acceleration have the same sign
When is the particle speeding up?
300
When a graph is increasing and concave down
When is f(x) increasing at a decreasing rate?
300
If f is continuous over closed interval and differentiable over the same open interval, then the instantaneous RoC = average RoC at least once
What is the Mean Value Theorem?
400
The limit of the sum/difference of two functions is the sum/difference of their limits. ex. 1.) lim [ f(x) + g(x) ] = lim f(x) + lim g(x) 2.)lim [ f(x) - g(x) ] = lim f(x) - lim g(x)
What is the sum/difference property of Integrals?
400
implies f is concave down
What is f"<0?
400
when velocity and acceleration have opposite sign
When is the particle slowing down?
400
When a graph is decreasing and concave up
When is f(x) decreasing at an increasing rate?
400
If f is continuous over closed interval, then a max and a min will occur at a critical value or endpts
What is the Extreme Value Theorem?
500
Bring constant out in front of the limit. example: lim(x->c)4 f(x)=4lim (x->c)f(x)
What is the constant multiple property of limits?
500
an inflection point can be found when this occurs
When does f"(x) change from positive to negative or negative to positive?
500
the the total distance a particle has traveled can be calculated by using the ________
What is the absolute value of velocity?
500
When a graph is decreasing and concave down
When is f(x) decreasing at a decreasing rate?
500
If f is continuous over closed interval, then every value b/t f(a) and f(b) exists