119Mdt1Solutions - Last Name Name Student No.: Department:...

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Unformatted text preview: Last Name Name Student No.: Department: Section: Signature: : : : : : : : : : : Code Acad.Year Semester Date Time Duration M E T U Northern Cyprus Campus Calculus and Analytical Geometry I. Midterm Math 119 2007-2008 Fall 2.11.2007 17:40 120 minutes 6 QUESTIONS ON 6 PAGES TOTAL 101 POINTS 1 2 3 4 5 6 1. (4+4+4+4=16 points) Evaluate each of the following limits if it exists, or else show why it doesn’t exist. (Do not use L’Hospital’s rule.) (a) lim x → 6 sin( x- 6) x 2- 36 = lim x → 6 sin( x- 6) x- 6 lim x → 6 1 x + 6 = 1 12 (b) lim x → 1 x 2 + 2 x- 3 x 2- 3 x + 2 = lim x → 1 ( x + 3)( x- 1) ( x- 2)( x- 1) = lim x → 1 ( x + 3) ( x- 2) =- 4 (c) lim x → ( x | x | + x | x | ) lim x →- ( x | x | + x | x | ) = lim x →- (- x 2 + x- x ) =- 1 lim x → + ( x | x | + x | x | ) = lim x → + ( x 2 + x x ) = 1 Since the left and right limits do not agree, the limit does not exist. (d) lim x → + ∞ ( √ x 6 + 5 x 3- x 3 ) = lim x → + ∞ ( √ x 6 + 5 x 3- x 3 ) ( √ x 6 + 5 x 3 + x 3 ) ( √ x 6 + 5 x 3 + x 3 ) = lim x → + ∞ x 6 + 5 x 3- x 6 ( √ x 6 + 5 x 3 + x 3 ) = lim x → + ∞ 5 x 3 x 3 ( q 1 + 5 x 3 + 1) = 5 2 2. (a) (10 points) Using the ²- δ definition of limit, prove that...
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This note was uploaded on 03/23/2011 for the course MAT 119 taught by Professor Various during the Spring '11 term at Middle East Technical University.

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119Mdt1Solutions - Last Name Name Student No.: Department:...

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