Answers vary (the limit of a function is the value that the function gets close to or reaches as x approaches a particular value)
100
If position is s(t), what do s'(t), s''(t), and s'''(t) represent?
What is velocity, acceleration, and jerk?
100
Give both definitions of derivative.
Ummmmm ....
100
Give the four steps of logarithmic differentiation.
1. take ln of both sides
2. differentiate both sides
3. solve for dy/dx
4. substitute for y
200
d/dx(secx)=
What is secxtanx
200
Explain why you cannot use substitution to find the limit:
lim (as x-->3) of the function 1/(x-3)
The function is not defined when x=3, therefore the limit does not exist.
200
What is speed (in terms of velocity)?
What is the absolute value of velocity?
200
Find the derivative of y = 4x^2 -3 when x = 2 using the definition of derivative (whichever definition you prefer).
What is 16?
200
Give the change of base theorem (log sub a of x)
What is ln(x)/ln(a)
300
cos(pi/6)=
What is (squareroot3)/2
300
What method do you generally use when finding the limit of a function as it approaches infinity?
What is end behavior model?
300
When velocity is equal to zero, what is the particle doing?
What is changing direction?
300
Find the derivative of y = (x^2-3x)^3
What is 6x^5 - 45x^4 + 72x^3 - 27x^2
300
Give the derivative of 6^x
What is 6^x (ln6)
400
pi/4 = how many degrees?
What is 45 degrees
400
Describe how to find horizontal asymptotes using limits.
If the limit of a function as it approaches infinity or negative infinity is a constant (call it b) , then y = b is a horizontal asymptote
400
When velocity is negative, what direction is the particle moving?
What is to the left?
400
Find dy/dx:
x^2y + 3x -2y = 67393
What is (-2xy-3)/(x^2-2)
400
Differentiate 3^cosx
What is (3^cosx)(ln3)(-sinx)
500
d/dx(secxtanx)
What is secx(tan^2x + sec^2x)
500
Describe how to find a vertical asymptote using limits.
If a right hand or left hand limit of a value (call it a) approaches positive or negative infinity, then x = a is a vertical asymptote
500
What is the difference between average rate of change and instantaneous rate of change?
Average rate of change: rate of change between two points (calculated using slope formula)
Instantaneous rate of change: the derivative of a function at a single point