This past week all we did was another set of AP tests and corrections.
The steps for related rates are:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
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
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*
Also I am going to talk about taking implicit derivatives. The steps for taking implicit derivatives are:
1. Take the derivative of both sides like you would normally do
2. Everytime the derivative of y is taken it needs to be notated with either y ' or dy/dx
3. Solve for dy/dx or y ' as if you are solving for x.
One problem am having is integrating something such as sin^2(x).
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okay, for sin^2(x)
ReplyDeletejust put the ^2 as the exponet of the x
so it would be sin(x)^2
integrate that as...[-cos(x)^2(2x)]
therefore the answer is
-2xcos(x)^2
hope this helps
~ElliE~
I just wanted to point out that it seems that integrating sin^2(x) is actually much harder than we've learned...I'm not sure though...
ReplyDeleteB-rob might want to comment on this one. (dylan's blogs)
This is a chain rule problem. Whenever you see a trig function raised to an exponent you use chain rule to work it. Rewrite it as [sin(x)]^2
ReplyDeleteBring the exponent to the front, then multiply it by the derivative of the inside just as you would in a chain rule.
This is chain rule bring the exponent to teh front and multiply by teh der of the inside.
ReplyDeletemake it sin(x)^2, and idk if it's the right way but then i just take the derivative of sin and multiply it by the derivative of x^2 or whatever..
ReplyDeleteYou can't use the chain rule in integration!!!!!!!
ReplyDeletebring the exponent to the front then multiply by the derivative...
ReplyDelete