Suppose you want lim x-> a [f(x) - f(a)](x-a) where a = 2

get [f(x) - f(a)](x-a) with a = 2, then take the limit as x -> 2

f(x) - f(a)/(x-a) =( 4.5x^2 -3x + 2 - (4.5(2)^2 - 3(2) + 2)]/(x- 2)

= (4.5x^2 - 3x + 2 - 14)/(x-2)

= (4.5x^2 -3x -12)/(x-2)

= (4.5x + 6)(x-2)/(x-2)

= 4.5x + 6

Now we take lim x-> 2 (4.5x + 6) = 4.5(2) + 6 = 15

## Friday, January 29, 2016

## Sunday, January 24, 2016

If the angle is negative in value, simply add 360 each time until you get a number between 0 and 360 and follow the same guidelines as above.

For example, an angle of -556 degrees would have it's terminal side in quadrant 2. Add 360 to -556 and you get -196, then add 360 again to get 164, which is a second quadrant angle

## Thursday, January 14, 2016

First know the first 3 powers of i

i^1 = sqrt(-1)

i^2 = -1

i^3 = -i

To get any power of i greater than 4, simply divide by 4 and the integer value remainder gives the answer. It will be one of the above.

Example:

i^45.... 45 divided by 4 is 11 with a remainder of 1, so the answer is sqrt(-1)

i^202..... 202 divided by 4 is 50 with a remainder of 2, so the answer is -1

i^79.... 79 divide by 4 is 19 with a remainder of 3, so the answer is -i

## Saturday, January 9, 2016

### Chi square test

Suppose the frequency tablef or the counties and votes for a particular candidate are as follows

Miami Dade 6

Broward 8

Palm Beach 34

Pinellas 10

Hillsbourough 8

Total is 66

Relative frequencies are each frequency divided by the total

Miami Dade = 6/66 = .09

Broward = 8/66 = .12

Palm Beach = 34/66 = .52

Pinellas = 10/56 = .18

Hillsborough = 8/66 = .12

b. If the votes were equal across each county, you'd expect 66/5 = 13.2 for each. So we get a X^2 statistic

(6 - 13.2)^2/13.2 + (8-13.2)^2/13.2 + (34-13.2)^2/13.2 + (10 - 13.2)^2/13.2 + (8-13.2)^2/13.2 = 41.59

The critical value for the test for X^2, 4df at alpha = .05 = 9.488

Since the 41.59 > 9.488 critical value, reject Ho

c. The conclusion is that there is significant evidence say that the proportion of voters for Buchanon is not the same across all the counties.

## Tuesday, January 5, 2016

sin^2 + cos^2 = 1

1 + tan^2 = sec^2

1 + cot^2 + csc^2

Also you need to know the derivatives of trig functions

sinx ..... derivative cosx

cosx..... derivative -sinx

tanx ......derivative sec^2 x

cotx .... derivative -csc^2 x

secx.... derivative tanxsecx

cscx .... derivative -cotxcscx

the trig identities come in handy to do substitutions to obtain antiderivatives.

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