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mid3_practice

# mid3_practice - Find the general indefnite integral(a[5...

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Math 1271, Lec 020: Calculus I Fall 2010 (Practice) Midterm Exam III Instructions Check that this booklet consists of 10 pages including the front page. To get full credit, you must show all steps in your solutions. Calculators are NOT allowed. You don’t need to simplify your answer. Good luck! Section and TA: Student ID: Name: Signature: Problems P 1 P 2 P 3 P 4 P 5 P 6 P 7 Total Scores 1

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Problem 1. [13 points] Find the dimensions of the rectangle of largest area that has its base on the x -axis and its other two vertices above the x -axis and lying on the parabola y = 9 - x 2 . 2
Problem 2. [10 points] Using Newton’s method with the first guess x 1 = 1, find the third approximation x 3 to the root of the equation x 3 - x - 2 = 0. You can leave your answer as a fraction. 3

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Problem 3. [14 points] Find the derivative of the following function. g ( x ) = integraldisplay x 2 x e t 2 + t t + 1 dt 4
Problem 4. Find the general indefinite integral. (a) [5 points] integraldisplay

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Unformatted text preview: Find the general indefnite integral. (a) [5 points] i 4-x 1 + x 2 dx (b) [5 points] i 4 x √ 1-x 4 dx 5 (c) [5 points] i (4 + ln x ) 2 x dx (d) [5 points] i sec 4 x tan x dx 6 Problem 5. Find the defnite integral. (a) [5 points] i 5 | x 2-2 x-3 | dx (b) [5 points] i 1 2(1 + x ) e x e + xe x dx 7 (c) [5 points] i 4 3 ( x-3) 23 dx (d) [5 points] i π/ 4-π/ 4 tan 7 x dx 8 Problem 6. [10 points] Evaluate the following limit. lim n →∞ 1 n p n √ e + n √ e 2 + ··· + n √ e n P 9 Problem 7. A particle is moving along a line with velocity v ( t ) = t 2-4 t + 3 (m/s). (a) [6 points] Find the displacement during the time interval 2 ≤ t ≤ 5. (b) [7 points] Find the total distance traveled by the particle during the time interval 2 ≤ t ≤ 5. 10...
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mid3_practice - Find the general indefnite integral(a[5...

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