Rules for Limits:…
1. if the degree of top equals the degree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0
linierazation:
The steps:
1. Determine the equation
2. f(x)+f`(x)dx
3. Figure out your dx
4. Figure out your x
5. Plug in everything
LRAM formula is:
delta x [f(a) + f( delta x +a) .... + f( delta x - b)]
EXAMPLE: calculate the left Riemann Sum for -4x -5 on the interval [-3, -1] divided into 2 subintervals.
delta x equals: -1+3 /2 = 2/2 = 1
1[ f(-3) + f(-3 +1)]
1[ f( -3) + f(-2)]
..plug into original equation.
RRAM formula is:
delta x [ f(a + delta x) + .... + f(b)]
so using the same example:
1[ f( -2) + f(-1)].. plug in to original equation.
MRAM formula is:
delta x [ f(mid) + f(mid) + .... ]
In order to find the midpoints, add the two numbers together then divide by two
In this problem the numbers would be: -3 , -2, -1
-3 + -2/ 2 = -5/2 and -2 + -1 / 2 = -3/2
so 1[f(-5/2) + f(-3/2)] and the plug in
Trapezoidal: multiply by delta x/2-
The formula: delta x/2 [f(a) + 2f(a + delta x) + 2f(a+ 2 delta x) + ....f(b)]
For this problem: 1/2 [ f(-3) + 2 f(-2) + f( -1)] and then plug in.
umm.. for what i don't understand, i really dont get what to do when i have to integrete a fraction, i keep forgetting.. i know i can't do quotient rule, but i just don't remember what i can do.
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one thing that you can do is if it is something like
ReplyDeletex+2
---
3
with one thing at the bottom you can separate it into
x 2
--- + ---
3 3
then take it from there
There are many ways to deal with fractions:
ReplyDelete1. Move the denominator to the top.
3/(x^2) 3(x^(-2))
2. Split up the fraction.
(x+15)/5 (x/5)+(15/5) (x/5)+3
3. Substitution.
2/((1+2x)^2) u=(1+2x) du=2
u^2 (1/3)(u^3) (1/3)((1+2x)^3)
These are just a few example of dealing with the integration of fractions.