Exam 1 Flashcards
When limits are at infinity and d>n what does f(x)=?
0
When limits are at infinity and d<n what does f(x) = ?
-infinity or infinity
When limits are at infinity and d=n what does f(x) =?
y=a/b ( coefficient of the numerator divided by the coefficient of the denominator.
what type of discontinuity is it if there is an empty circle?
Hole
What type of discontinuity is it if it is a filled in circle?
removable
What type of discontinuity is it if there is no hole and both sides never end?
Infinite
When is there a vertical asymptote?
When the denominator is zero and does not cancel out with the numerator.
When can you tell there is a hole from just the function?
When the denominator is zero but can be canceled out with the numerator.
When you are asked for the average rate of change what formula do you use?
Rise/run
When asked about how fast or the instantaneous rate of change what do you do?
Find the derivative and then sub in the numbers.
What is the derivative of any constant?
0
What is the power rule?
nx^n-1
what is the derivative of e^x?
e^x
What is the derivative of any exponential base function?
In(a)a^x
What’s the derivative of a natural log func? (y=in(x))
1/x or x^-1
What is the chain rule of In derivitive? (y=In(f(x))
y prime= The derivative of the function/ the original function.
What is the chain rule for the exponential functions? ( e^f(x)
Its the derivative of whatever function e is raised to Infront of the entire original exponential function.
Product rule
(ex. (3x+2)(5x-1)
Find the derivative of the first one multiplied by the second original function + the first original function multiplied by the derivative of the second one.
quotient rule
(ex. x^5-6x/x^3=4)
same as the product puling except subtracting and that goes in the numerator over the orginal denominator squared
Before finding the equation of a tangent line you have to what?
Find the derivative
