## Sunday, January 31, 2010

### I see math!

Continuous and Differentiable!

No breaks or discontinuities in the line.

Continuous but not Differentiable!

Cusps are not differentiable

Non Continuous, Non Differentiable!

Jump discontinuity

Invertible!

This function still passes the vertical line test if it is inverted

Not one-to-one!

Circles are not one-to-one

No breaks or discontinuities in the line.

Continuous but not Differentiable!

Cusps are not differentiable

Non Continuous, Non Differentiable!

Jump discontinuity

Invertible!

This function still passes the vertical line test if it is inverted

Not one-to-one!

Circles are not one-to-one

### Choices

1. For any point (a,b) on an invertible function, the derivative of the inverse of the function evaluated at b is equal to the reciprocal of the derivative of the function evaluated at a. In other words, the derivative of the inverse of a function is the reciprocal of the derivative of the function.

2. In symbols:

3. The function for volume of a sphere is below:

Yes, volume is an invertible function.

4.The inverse of this function:

5.

6. The slope of the tangent of the red function is 11.36, and I found the slope of the green function is .088, which is equal to 1/11.36.

7.I chose not to go to class. I've never done a virtual class before, so I wanted to see if I could effectively learn the class material without actually going to class. Also, by taking the virtual class I was able to sleep in, (this was really just a nice bonus). By utilizing my tools on the internet, I was able to learn the subject matter. The scribe post was also a very helpful tool. Overall, I think I was able to learn just as well in the virtual class, but had this been a more complicated, difficult topic, it's definitely helpful to have a teacher who knows what they are talking about.

2. In symbols:

3. The function for volume of a sphere is below:

Yes, volume is an invertible function.

4.The inverse of this function:

5.

6. The slope of the tangent of the red function is 11.36, and I found the slope of the green function is .088, which is equal to 1/11.36.

7.I chose not to go to class. I've never done a virtual class before, so I wanted to see if I could effectively learn the class material without actually going to class. Also, by taking the virtual class I was able to sleep in, (this was really just a nice bonus). By utilizing my tools on the internet, I was able to learn the subject matter. The scribe post was also a very helpful tool. Overall, I think I was able to learn just as well in the virtual class, but had this been a more complicated, difficult topic, it's definitely helpful to have a teacher who knows what they are talking about.

### I see math

## Saturday, January 30, 2010

### See Math

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