velocity/acceleration/distance
How do you find velocity given position?
Take the derivative.
What is another name for a derivative?
What is another word for antiderivate?
Integral.
When does a limit exist?
When left and right hand sides agree.
This operator undoes a derivative, giving the original function from the derivative.
What is an integral/antiderivative?
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.
What law is used when a limit equals 0/0?
L'Hopital's Rule.
The second derivative of position.
What is acceleration?
How do you find acceleration given position?
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.
The derivative of tan(x).
What is sec2(x)?
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.
What happens if the limit is going to infinity and the top exponent is greater than the bottom one?
DNE.
Find the definite integral of 4x3 from 1 to 4.
255
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 it asks you how much, how many, total, etc.
Integrate!
Lim (x2-x-2)/(x2-2x)
x-> 1
2.
Find d/dx of 1/x
simplify your answer.
What is ln(x)?