post 21

The steps for working linearization problems are:
1. Identify the equation
2. Use the formula f(x)+f ' (x)dx
3. Determine your dx in the problem
4. Then determine your x in the problem
5. Plug in everything you get
6. Solve the equation

Example problem:(sr=square root) Use differentiability to approximate sr(4.5)
f(x)=sr(x) sr(4)+(1/2 sr(4) )(.5)=1.125sr(x)+(1/2 sr(x) )
dx error=.005
dx=.5
x=4

The next topic I will talk about is integration. Integration finds the area under a curve. The Riemann sum approximates the area using the rectangles or trapezoids. The Riemanns Sums are:
LRAM-Left hand approximation=delta x[f(a)+f(a+delta x)+...f(b-delta x)]
RRAM-Right hand approximation=delta x[f(a+delta x)+...f(b)]
MRAM-Middle approximation=delta x[f(mid)+f(mid)+...]
Trapezoidal-delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
delta x=b-a/number of subintervals

Example problem: Find the area of f(x)x-3 on the interval [0,2] with 4 subintervals.

delta x=2-0/4=1/2
LRAM=1/2[f(0)+f(1/2)+f(1)+f(3/2)]1/2[-3+-5/2+-2+-3/2]1/2[-9]= -9/2
RRAM=1/2[f(1/2)+f(1)+(3/2)+f(2)]1/2[-5/2+-2+-3/2+-1]1/2[-7]= -7/2
MRAM=1/2[f(1/4)+f(3/4)+f(5/4)+f(7/4)]1/2[-11/4+-9/4+-7/4+-5/4]1/2[-8]=4
Trapezoidal=1/4[f(0)+2f(1/2)+2f(1)+2f(7/2)+f(2)]1/4[-3+-10/2+-4+-6/2+-1]1/4[-16]= 4

For things I do not know I forgot how to do problems that ask to find acceleration and velocity when all that is given is postitions and an equation of t(x). This is what my wiki was on and failed it horribly because I have no idea what I am doing.