First Holiday Post

Hope everyone had a great Christmas and has a excellent New Year.


So we started off the year going over pre-calculus from last year and learning the basics of derivatives.


So, taking limits:


If the equation is an infinite limit, and it is a fraction, then you use the degree to find the limit.

- If the largets degrees of the top and bottom are equal to each other, then use the the coefficients of the largest degrees in fraction form... simplify if necessary.

- If the degree of the top is larger than the degree of the bottom, then the limit is positive or negative infinity, depending on your coefficients.

- If the degree of the top is smaller than the degree of the bottom, then the limit is 0.



And when I was stressing when we first were learning derivatives, now they are almost natural to me...

Example of taking derivatives:

3x^2 + 5x + 212309483290781075843157834097175173847534

You take the derivates using the exponents and get:

(3)(2)x + 5

= 6x + 5

Example 2:

2/x^2

you use the quotient rule { [copybottom*deriv.top - copytop*deriv.bottom] / bottom^2}

[(x^2)(0) - (2)(2x)] / (x^2)^2

Simplify:
= -4x / x^4

Simplify:

-4/x^3

Example 3:

tan(x/3)

Can also be written as: tan(1/3*x)

take derivative: sec^2(1/3*x) * (1/3)

Simplify: [sec^2(x/3)]/[3]

Example 4:

5x^8 + 9x^7 - x^6 + 78x^5 + 8x^4 - 10x^3 + 56x^2 - 23x + 9*23*1993

Pretty much felt like busting my calculator out :)...

Anyway:

40x^7 + 63x^6 - 6x^5 + 390x^4 + 32x^3 - 30x^2 + 112x - 23

Well I guess that's it for this post and once again:

Merry Christmas and Happy New Year!!!