Post #18

Calculus Week #18

So exams are finally over..thank god, and the holidays are here :-)

As to what I'm going to explain... I really don't know what to explain anymore. I've really explained a LOT of different things..

limits as x goes to infinity with fractions...
1. If the degree on top is larger than degree on bottom, it’s infinity.
2. If the degree on top is equal to the degree on bottom, divide the coefficients.
3. If the degree on top is smaller than degree on bottom, it’s 0.

Let's see...implicits are easy
1. take the derivative of both sides
2. every time you take the derivative of y write it with dy/dx
3. solve for dy/dx

Related Rates
Identify all variable and equations.
Identify what you are looking for.
Make a sketch and label.
Write an equation involving your variables. Know that you can only have one unknown variable, so a secondary equation may be given.
Take the derivative with respect to time. aka: (dy/dt) or (dx/dt).
Substitute in derivative and solve for the rate.

Limit as x goes to infinity of
sin(nx)/a

is n/a.


e^x integration is easy... Whenever working with e^x integration, your u is always set to the exponent of the e. The derivative of e^x is simply e^x times the derivative of x. So when working with these, really all you have to worry about it balancing it out with the derivative of x.

For example, e^(2x). This would become (1/2)e^(2x) + c, The reason behind the (1/2) is because if you take the derivative of e^(2x) it is 2e^(2x). However, we don't want that 2. So we take it out by putting a (1/2) in front, just like we did for other integrals.


good enough for now.