calculus help

[jerry123]

I can't figure out how to approach these problems. could someone please help me?

http://postimage.org/image/sq1hzx0zb/

1. what is the area of the smallest rectangle the can be circumscribed around the unit circle?
2. what is the area of the largest rectangle that can be inscribed within the unit circle?
3. approximate the area of the unit circle using an appropriate number of circumscribed rectangles if width 0.4 units.
4. approximate the area of the unit circle using an appropriate number of inscribed rectangles if width 0.4 units.

There are more questions, but if I can get help on these, I will be able to do the rest myself.

 

[JeffM]

I can't figure out how to approach these problems. could someone please help me?

http://postimage.org/image/sq1hzx0zb/

1. what is the area of the smallest rectangle the can be circumscribed around the unit circle?
2. what is the area of the largest rectangle that can be inscribed within the unit circle?
3. approximate the area of the unit circle using an appropriate number of circumscribed rectangles if width 0.4 units.
4. approximate the area of the unit circle using an appropriate number of inscribed rectangles if width 0.4 units.

There are more questions, but if I can get help on these, I will be able to do the rest myself.

Questions 3 and 4 are very badly worded.

I presume questions 1 is not giving you a headache. Question 2 is a pretty straight foward problem in differential calculus; are you having problems with it? If so what are your specific questions?

Questions 3 and 4 make no sense to me as worded. I think what they are getting at is to approximate the area of the unit circle with rectangles of width 0.4 that, for question 3, are partly outside the circle and, for question 4, entirely inside the circle. Does that seem to make sense in context?

In our Read Before Posting thread, we ask that you explain where you are in your math studies. This sort of looks like a transitional exercise between differential and integral calculus. Is that where you are? Alternatively, this may be an example of Archimedes' method of exhaustion, an early but big step on the way to integral calculus, that might come up in a very odd history of mathematics class.

 

[jerry123]

We just finished covering anti-derivatives and integrals.

 

[MarkFL]

Questions 3 and 4 are very badly worded...Questions 3 and 4 make no sense to me as worded...

I agree completely here. I am assuming they are trying to get you to utilize Riemann and Lebesgue type summations, but they are indeed worded very badly. Calculus can be challenging enough for a student without having to suffer such poorly worded problems.

 

[JeffM]

We just finished covering anti-derivatives and integrals.

In that case, I think the best bet is to approximate in question 3 with non-overlapping rectangles of width 0.4 that lie parly outside the unit circle and to approximate in question 4 with non-overlapping rectangles of width 0.4 that lie entirely within the circle. I cannot promise you that that is the right approach to such badly worded questions.

 

[srmichael]

In that case, I think the best bet is to approximate in question 3 with non-overlapping rectangles of width 0.4 that lie parly outside the unit circle and to approximate in question 4 with non-overlapping rectangles of width 0.4 that lie entirely within the circle. I cannot promise you that that is the right approach to such badly worded questions.

This is most likely what they are asking. In other words, the circumscribed rectangles is the Upper Sum and the inscribed rectangles is the Lower Sum.