91E2P2 - a) Z dx x ( x-1) 2 = b) Z 3 x + 7 x 2 + 4 x + 5 dx...

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2 2. Find the limits of the following functions . Indicate the reasoning behind your answer. a) lim x 0 + sin x x 2 = b) lim x 0 + x x = 3. Find 1 Z - 1 dx x 2 =
3 4. Evaluate the following integrals.

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Unformatted text preview: a) Z dx x ( x-1) 2 = b) Z 3 x + 7 x 2 + 4 x + 5 dx = ~ show your work on the back of the previous page. ~ hint: split up into two integrals 4 5. Recently, we have often computed that Z sec 3 x dx = 1 2 sec x tan x + 1 2 ln | sec x + tan x | + C Using this fact, nd R sec 5 x dx = 5 6. a) Find the total area of the region bounded inside the ellipse x 2 a 2 + y 2 b 2 = 1 . ~ hint 1: make a rough sketch and use symmetry ~ hint 2: total area means to view the area under the x-axis as positive so that your answer will not be 0. ~ hint 3: you may use the formula R cos 2 x dx = 1 2 x + 1 4 sin2 x + C . ~ hint 4: this is easier than you think . ... Answer: The total area bounded by an ellipse is: b) What happens to the total area when the number a approaches the number b? Why does this not surprise you?...
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This note was uploaded on 12/13/2011 for the course MATH 142 taught by Professor Kustin during the Fall '11 term at South Carolina.

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91E2P2 - a) Z dx x ( x-1) 2 = b) Z 3 x + 7 x 2 + 4 x + 5 dx...

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