Derivatives
The power rule
what is d/dx (ax^n)=nax^n-1
The value of the constant
What is the limit of a constant
y=p/q
What is a rational function
This is the derivative of a position-time graph
The definition of absolute value
What is the absolute value of x is equal to x if x is greater than or equal to zero, the absolute value of x is -x if x is less than zero
The quotient rule
vertical asymptote, discontinuity, hole, places where the graph ceases to exist (limited domain)
Where do limits not exist
This asymptote can never be crossed
What are vertical asymptotes
The derivative of velocity
What is acceleration
f(x) = f(-x)
What is an even function
Where is there no derivative
This limit approaches zero and = 1 and we have to memorize it
What is the limit as x approaches zero of (sin(x))/x
The denominator has a power greater than or equal to the numerator
When is there a horizontal asymptote
The maximum height of free fall
When is the 1st derivative equal to zero
f(x)=-f(-x)
What is an odd function
The derivative of sin(cos(tan(x2)))
What is cos(cos(tan(x2)))(-sin(tan(x2))(sec2(x2)(2x)
This limit approaches zero and = zero and we have to memorize it
What is the limit as x approaches zero of (cos(x)-1)/x
There is an x in the denominator that cannot be divided out
When is there a vertical asymptote
This is the force of gravity on earth
What is -9.81 m/s2
This is the definition of continuous.
When a function is continuous at point a if f(a) is defined, the limit as x approaches a is defined and the limit as x approaches a is equal to f(a)
The definition of a derivative of a function
What is the derivative of a function denoted y' is equal to the limit as delta x approaches 0 of (f(x+delta x) -f(x) )/delta x
What is the limit as x approaches c of f(x) = L exists iff for all epsilon greater than zero there exists a delta greater than zero such that the absolute value of f(x)-L is less than epsilon whenever the absolute value of x-c is less than delta
divide the numerator by the denominator
How to find an oblique asymptote
This is a sudden change in acceleration
What is a jerk
This is what you do with the h after using the definition of derivative
What is setting h equal to zero