108Fall12Ex1VersionA

5 5 given by the integral 1 4 dx x 05

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Unformatted text preview: dx with a substitution, what would be a good x − x +1 2 choice for u? a) x 2 − x + 1 c) x 2 ) d) cos csc 3 b) x − 1 d) x − 1 2 1 MthSc 108 Test 1-Version A Fall 2012 4. (3 pts.) Which of the following is NOT true regarding the regions depicted in the graph below? 5+ 5 6 a) A = ∫ [ f ( x ) − g( x )] dx b) A + B + C = 7 c) B = ∫ [ g( x ) − h( x )] dx 3 f ( x ) dx A+ B = ∫ [ f ( x ) − h( x )] dx 2 3 5 d) ∫ 5− 5 4 5. (3 pts.) Find the equation of a curve that passes through the point (1, e) and has an arc 5 2 length on the interval [ 0.5, 5 ] given by the integral ∫ 1 + 4 dx . x 0.5 2 a) y = e + 2 − 4 x b) y = e − 2 + c) y = e + 2 − 2 x2 2 x4 d) y = e + 2 − 2 x x 6. 1 (3 pts.) The natural logarithm of x is defined by ln x = ∫ dt for x > 0 . Using this t 1 definition, which of the following theorems allows us to conclude that d ln x 1 = ? dx x a) Mean Value Theorem b) Fundamental Theorem of Calculus c) Chain Rule d) Intermediate Value Theorem () 2 MthSc 108 Test 1-Version A Fall 2012 7. Find the derivative of y with respect to x for y = x ln x . (3 pts.) ⎛ 2⎞ ln x ln x−1 a) y′ = x ln x ⎜ ⎟ x b) y ′ = ⎝ x⎠ x ⎛ 2 ln x ⎞ x ln x−1 c) y′ = x ln x ⎜ d) y ′ = ⎝ x ⎟ ...
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This note was uploaded on 10/17/2013 for the course MTHS 1080 taught by Professor Briggs during the Fall '13 term at Clemson.

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