Post #37?

Well I was actually just studying..so I'm going to go over some random things.

Area formula: aSb top - bottom
Volume formula: (pi) aSb (top)^2 - (bottom)^2
QUESTION: when do you use aSb (top-bottom)^2?

limit rules as x--> infinity are really simple:
top degree = bottom degree-->divide coeffient
top degree < bottom degree-->0
top degree > bottom degree-->infinity

remember:

increasing/decreasing, max/min is FIRST derivative test
concave up/down, pt of inflection is SECOND derivative test

if original graph is postive then the deivative graph is increasing
if original graph is negative then the deivative graph is decreasing
QUESTION: how do you know if it is concave up/down?

for a piecewise the derivatives must equal in order for it to be differentiable

something I just learned:

d/dx (integral from 0 to x^2 (sin(t^3) dt)
= x^2[sinx^6]
*pull the top bound out to the front and plug in t^3 for x

tangent lines:
take derivative
set = to 0
solve for x
plug into point slope formula
*linearzation is much like tangent lines

average value:
1/b-a (aSb) equation

Mean Value Theorem:
plug in points to original equation
take those points you just found and the point given in problem to find slope
take derivative of orginial equation and set = to the slope

Position, Velocity, Acceleration:
P--> Postion
V--> Velocity
A--> Acceleration
*Going down take derivative; going up take integral

Calculator:
change direction-zeros on graph
bounds for integral-intersection on graph
graph stuff!

and:
a corner IS continuous but NOT differentiable
don't forget +C

I'm still worried about substitution & ln integration!