velocity/acceleration/distance
How do you find velocity given position?
Take the derivative.
What is another name for a derivative?
Instantaneous rate of change.
What is another form of antiderivates?
Integral.
When does a limit exist?
When left and right hand sides agree.
What is the formula for average value?
(1/b-a) int(f(x))dx
How do you find velocity given acceleration?
Take the antiderivate.
What is the derivative of 2x?
2.
What can't you forget when writing an antiderivative with an open integral?
+C.
L'Hopital's Rule.
When is a particle/object's speed increasing?
Velocity and acceleration are the same sign
How do you find acceleration given position?
Take the second derivative
What is the derivative of 4x6?
24x5.
What is the antiderivative of 4x?
2x2+C.
When a limit is going to infinity, what do you look at first?
The exponents.
What is the inverse trig function of tan(x)?
(1)/(1+x2).
Initial condition + displacement.
What are the steps in the chain rule?
Outside in (power, trig, angle).
What is the antiderivative of 7x5?
(7/6)x6 + C
What happens if the limit is going to infinity and the top exponent is greater than the bottom one?
+- infinity
On the graph of f'(x), how can we tell if a point is a relative maximum?
It crosses the x-axis from positive to negative.
Position of a particle at x=0 is given by the equation 5x2+8. What is the particles velocity at t=0
10x.
What is the derivative of (sin(4x))7?
28sin(4x)6(cos(4x)).
What do you do when asked how much, how many, total number of, etc.
Integrate it!
Lim (x2-x-2)/(x2-2x)
x-> 1
2.
What is Rolle's Theorem?
Let f be differentiable on (a, b) and continuous on
[a, b]. If f(a) = f(b), then there is at least one
number c in (a, b) such that f ‘(c) = 0.