Suppose you want to determine the area bounded by two curves denoted by functions f(x) and g(x).

We find the points of intersection by setting f(x) = g(x). Then we determine which curve is the upper curve in the integral and which is the lower curve in the integral. Suppose the points of intersection are x=1 and x=3.

If f(x) is the upper curve then the integral looks like

Integral (1 to 3) [f(x) - g(x)] dx

If g(x) is the upper curve the the integral looks like

Integral (1 to 3) [g(x) - f(x)] dx

## Tuesday, March 31, 2015

## Saturday, March 28, 2015

https://learnivore.com/instructors/mathematics-help-with-tutor-with-15-years-experience

https://www.fiverr.com/mathtutorkk

## Saturday, March 21, 2015

If we pick two angles from the unit circle that add to 165, we can obtain the exact value for sin(165). The reason is we can substitute those values in for this formula.

sin(a + b) = sin(a)cos(b)+cos(a)sin(b)

Notice that 120 + 45 = 165 and both of those values are on the unit circle

sin(120 + 45)= sin(120)cos(45) + cos(120)sin(45)

= (sqrt(3)/2)(sqrt(2)/2) + (-1/2)(sqrt(2)/2)

= sqrt(6)/4 - sqrt(2)/4

= (sqrt(6) - sqrt(2))/4

## Wednesday, March 18, 2015

The Most Simple Introduction to Hypothesis Testing

## Thursday, March 12, 2015

For example, suppose you want a 95 percent confidence interval for the sample mean. The formula is mean +/- standard error which is Z(alpha/2)standard deviation/square root(n). alpha is 1-.95 = .05. So the Z value is 1.96.

Now if we want an x value that 95% of the data falls below, then we need Z(.05) which is 1.645.

Be careful to understand the difference between the two.

## Friday, March 6, 2015

The first derivative f'(x) = 2x + 3

Second derivative f"(x) = 2

Notice the second derivative is positive for all values of x therefore the function is concave up, therefore opening up.

## Tuesday, March 3, 2015

For example, suppose the radius of a circle is 6 and the angle of the sector is 45 degrees. Therefore the area of the sector is

(45/360)Pi(6)(6) = (1/9)(36)Pi = 14.14

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