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Calculus/Volume of revolution

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Expert: - 2/14/2010


Question

Calculus Questions
Sir, As questions are calculus questions and written with the help of Math type so, I attached the image of questions from Office. Please see attached image for questions.

Answer

Volume of revolution
Questioner: vampire
Country: Pakistan
Category: Calculus
Private: No
Subject: Calculus questions again
Question:

Please see attached image for questions.  

...................................
1. The region is shown in my diagram.

Your 'disk' element has

r = y = x^2

V = pi r^2 dx = pi x^4 dx

and you integrate from x = 0 to x = 3.

That should do it.

2. When you use l'Hospital's rule, you will differentiate top and bottom as many times as needed.  In this case, when you do it twice, you will get:
             2
lim        -----  --> 0
x-> inf      6x

That's the answer.

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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