post # 30

alright, so this week we took more ap tests. and went over them not only in class but also with alex in fifth hour. it actually did help a lot

FINDING AREA BETWEEN A CURVE:
The formula you use is b(int)a (top eq.) - (bottom eq.).If a and b is not already given to you, then you much set the equations equal to each other and solve.You find which equation is top/bottom by graphing both and simply looking to see which one is on top.If the area is on the y-axis, then the a and b values need to be set as y-values, and the equations must be solved for x.

KEYWORDS:
Local minimum- first derivative, set equal to zero, solve, set up intervals and check
Maximum speed- absolute value of velocity
Linearization- find the equation of the tangent line (APPROXIMATE)
Lim h> 0 + h – definition of derivative- take derivative of what is behind the parenthesis
Maximum acceleration- find the maximum slope
Starting point- original function; zeros of velocity will give you max and mins
Rate- take derivative

AVG VALUE:
1/b-a (int) f(x)
it usually gives you an interval. it will say on interval from [1,4]
1 goes on bottom of integral & 4 goes on top => a = 1 , b = 4

this week we had instantaneous rate of change on our ap tests, something we haven't seen in a while! i know alex went over it in 5th hour the other day, but i missed it. can someone go over that for me?
i also need help with particle problems.
OH and i recently found out that the integral of sin^2(x) is a trig identity. if someone could go over the trig identities that would be VERY helpful