Well sadly, the holidays are over. Anyways, lets get straight to the blog.
I'm going to review some of the basics.
FORMULAS FOR DERIVATIVES:
We can all take derivatives. They are really easy, but some are easily forgotten
a^x = lna(a^x)
e^x = e^x
lnx = 1/x
tanx = sec^2x
cscx = -cscxcotx
secx= secxtanx
cotx = -csc^2x
DEALING WITH GRAPHS:
1st derivative: Increasing, Decreasing, max and mins
2nd derivative: Concave up, Concave down, point of inflection.
RELATED RATES:
First, some of the formulas dealing with related rates.
CONE- V=3/4(pi)(h)(r^2)
CUBE- V=E^3
RECTANGLE- A=1/2(B)(H)
SQUARE- A=L x W P=2(L+W)
SPHER- V=1/3(pi)(r^3)
CIRCLE- A=2(pi)(r)
Now for an example:
The radius, r, of a circle is increasing at a rate of 3 centimeters per minute. Find the rate of change of area, A, when the radius is 5.
First I write down my given:
A =pir^2
dr/dt = 3
r = 5
dA/dt = ?
So take the derivative of the formula.
dA/dt=pi2r(dr/dt)
now plug in:
dA/dt = pi(2)(5)(3)
dA/dt = 30pi
I still mess up with integration!
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The trick for integration is to be able to either recognize the formulas or use substitution really. I can't really help you understand the whole INTEGRATION thing...you know??
ReplyDeleteOk, with integration, just remember it's doing what you can to undo a derivative. It's the opposite of a derivative. You also need to remember that in integration, there are no chain rules, product rules, or quotient rules, so you will need to use substitution to force the integral to work. For substitution, you'll have two parts: a derivative and an "origional function." You will use the "origional function" for u and it's derivative as du. Ln integration is also easy. It's when the the derivative of the bottom is the top, making u the bottom. the integral is then ln |u| (and + c depending on if it's infinite or finite).
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