# test2_1501_Fall2012.pdf

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Georgia Institute of Technology

Mathematics

MATH 1501

Liu

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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