So...it's the 32nd week of school...wait 9X4=36....4 more weeks left? What?? I think my math is off...
So, those substitution packets really kicked my butt!! I found out that I have no idea how to do it! I tried working on them this weekend and got nowhere! I learned it, and I used to be good at it...I'm just horrible now. Along with everything else...did anyone else forget everything? =/
I'm going to try to explain something...but don't take my word for it! =]
Product Rule.
Formula: (Derivative of the first)(the original second)+(The original first)(Derivative of the second)
Step 1: Obviously, you do the formula.
Step 2: Simplify! :)
Example: 3xy+z^2 (let's ignore the dx/dx, dy/dx, and dz/dx for simplicity, kay?)
Step 1: (3)(y)+(3x)(1)+2z
Step 2: 3y+3x+2z
Quotient Rule.
Formula: (Derivative of the top)(the original bottom)-(the original top)(derivative of the bottom)/(bottom)^2
Step 1: You do the formula.
Step 2: Simplify!
Example: 3x^2-x/4x
Step 1: (6x-1)(4x)-(3x^2)(4)/(4x)^2
Step 2: (24x^2-4x-12x^2)/(4x^2)
(12x^2-4x)/(4x^2)
Or you can simplify it completely:
3-1/x
A common mistake is to change the + and the - on those two! Don't get them mixed up!!!
For things I need help on:
Just about everything...I think I'm just going to go through all of the blogs a thousand times and hope that something clicks =/
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well, The Riemanns Sums always seem to trick me..so:
ReplyDeleteLRAM-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 Rule = delta x/2[f(a)+2f(a+delta x)+2f(a+2 delta x)+...f(b)]
&&&&&
delta x = b-a/number of subintervals
Here are some tips for the acceleration and velocity problems. If they give you acceleration and ask for veolocity, you integrate the function, you may also have to solve for C. So if they give you two numbers at the end. You plug in one for x and the other you set the function equal to and solve. If they ask for position, you integrate and follow the same steps again. Hope this helps!
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