# test3_1501_Fall2012.pdf

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Georgia Institute of Technology

Mathematics

MATH 1501

Liu

Fall

Description

Math 1501 K1-K4 L1-L4 Test 3 Total: 20 points
Section:
Name:
Student Number:
Fill in the blanks. Make sure to write down your procedure
clearly for problems (7)-(12).
(1) Let f(x) be a contiuous function on R. Express the limit as a deﬁnite
integral.
1
n→∞ n [f(1/n) + f(2/n) + ··· + f(n/n)] = ( ).
(1 point).
R R
(2) Given that 5f(x) dx = 7, 6 f(x) dx = 11,
R5 2 2
6 f(x) dx = ( ). (1 point).
(3) Set
Z x2 1
F(x) = dt,
x 1 + t2
′
F (1) = ( ). (1 point).
(4) Z π
2
|sinx| dx = ( ).
− 2
(2 points).
′ p 2
(5) Deﬁne a function F such that F (x) = 1 + sin x and F(π) = 3.
F(x) = ( ). (F could contain an integral and you don’t need to
evaluate the integral). (1 point).

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