141ex1samA - MATH 141 141E 141H EXAM I SAMPLE A 1 Let f x =...

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Unformatted text preview: MATH 141, 141E, 141H EXAM I SAMPLE A 1. Let f ( x ) = 4 x + cos πx . Find ( f- 1 ) (3). a) 1 4 b) 1 4- π c) 4- π d) 1 12 e) Cannot be determined 2. Evaluate the integral Z e 2 e 2ln x x dx . a) 4 b) 1 c) e 2 d) 3 e) e 4- e 2 3. Given that a,b > 0 and a 6 = b , evaluate lim x →∞ [ln(3+ ax )- ln(2+ bx )] . a) 0 b) ln a b c) ln 3 2 d) ∞ e)-∞ 4. Differentiate the function y = ln(sin(ln x )). a) 1 x sin(ln x ) b) cot(ln x ) x c) cot x + 1 x ln x d) 1 sin(ln x ) e) cot(ln x ) 5. Which of the statements below is/are true? (i) lim x →-∞ tan- 1 x =- π 2 (ii) cos(tan- 1 x ) = 1 √ x 2 + 1 (iii) s a) i only b) ii and iii only c) i and ii only d) None of the statements are true. e) All of the statements are true. 6. Find f ( x ), given f ( x ) = arcsin(cos(2 x )). ≤ x ≤ π 2 a)- 2 sin(2 x ) b)- 2tan(2 x ) c) 2 d)- 2 e)- 2 sin 2 (2 x ) 7. Evaluate the integral Z 5 x x + 10 dx . a) 25 4 b) 5 + 10ln5 c) 10- 5ln10 d) 5- 10ln5 e) 5 + 10ln 2 3 8. Evaluate the integral Z ln 2 e x √...
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This note was uploaded on 02/15/2010 for the course PHYS 211 taught by Professor Staff during the Spring '08 term at Penn State.

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141ex1samA - MATH 141 141E 141H EXAM I SAMPLE A 1 Let f x =...

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