test4math1501_solutions

test4math1501_solutions - Georgia Tech FALL 2009 Heinrich...

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Unformatted text preview: Georgia Tech FALL 2009 Heinrich Matzinger SOLUTION SET for QUIZ 4 FOR MATH 1501. • First name: last name Gtid • Close book, no calculators allowed. Full 50 minutes time. Show your calculations! Do not use Hospital’s rule! 1) Let f ( . ) be a continuous function defined on the domain [ a, b ], where a < b . Let F ( x ) denote the integral F ( x ) = integraldisplay x a f ( s ) ds, where x is in the interval [ a, b ]. Explain why F ( x ) ′ = f ( x ). Answer: Check out theorem 5.3.5 in your book. 2) What is the limit lim x → 2 + sin ( x − 2) x 2 − 4 equal to? Why? Answer: Let y = x- 2. As x goes to 2, we have that y goes to 0. Now, we have lim x → 2 + sin ( x- 2) x 2- 4 = lim x → 2 + sin ( x- 2) ( x- 2)( x + 2) = = lim x → 2 + sin ( x- 2) ( x- 2) · lim x → 2 + 1 ( x + 2) = lim y → sin ( y ) y lim x → 2 + 1 ( x + 2) = 1 · 1 4 = 1 4 3) What is the limit lim x → 3 + x 2 − 5 x +6 x − 3 equal to? Why? Answer: lim x → 3 + x 2 − 5 x +6 x − 3 = lim x → 3 +...
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test4math1501_solutions - Georgia Tech FALL 2009 Heinrich...

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