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# test2_1501_Fall2012.pdf

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School
Georgia Institute of Technology
Department
Mathematics
Course
MATH 1501
Professor
Liu
Semester
Fall

Description
Math 1501 K1-K4 L1-L4 Test 2 Total: 20 points Section: Name: Student Number: For problems (1.1)-(1.9), ﬁll in the blanks. ( If the result doesn’t exist, ﬁll in ”D.N.E.”) (1.1) sinx − x lim 3 = ( ). x→0 x (1 point). √ (1.2) f(x) = x − 2x + 1, f (0) = ( ). (1 point). (1.3) y = f(x) = 1 + x , (f −1 ) (2) = ( ). (1 point). (1.4) If xy + y = 1, then at the point (x,y) = (0,−1), dy = ( ), 2 dx and dx2 = ( ). (2 points). 3 (1.5) f(x) = x . f(x) takes on local minima at x = ( ); f(x) takes x+2 on local maxima at x = ( ); (2 points). 4 (1.6) f(x) = x (x − 5) has the point(s) of inﬂection at x = ( ). (1 point). (1.7) f(x) = (|x + 1|) 1/3. Determine whether or not the graph of f has a vertical tangent or vertical cusp at x = −1. ( ). (1 point). 1 1/3 (1.8) The lineariza
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