test1sample

# test1sample - - , say so. (5 pts each): a. lim x 1 x 2-3 x...

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R McDougal Name: Math 151N 12 July 2005 Test I Sample Instructions: Answer each question as completely as you can; remember you must show all work for full credit. Partial credit may be given for incorrect answers with work; no credit will be given for incorrect answers without work. If you must use a theorem, be sure to verify that all of its hypotheses are satisﬁed. Please write as legibly as possible. For you to receive points, I must be able to read your solutions. If there is any danger of confusion, please circle your ﬁnal answer. Please write all answers in the space provided. If you must continue your work in a dif- ferent location, please mark your work accordingly. Calculators are permitted subject to the restrictions stated in the syllabus. You may not consult books, notes, or each other for this quiz. Good luck! Problem Value Score 1 9 2 15 3 12 4 16 5 12 6 12 7 12 8 12 total 100

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1. Suppose ϑ is an angle in the ﬁrst quadrant and tan ϑ = 3 4 . Find (3 pts each): a. sin ϑ = b. cos ϑ = c. sec ϑ = 2. Evaluate the following limits. If the limit is or

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Unformatted text preview: - , say so. (5 pts each): a. lim x 1 x 2-3 x + 2 + ( x-1) cos( x-1) x-1 = b. lim x 2 + 3 x 2 x 2-x-2 = c. lim x 3 x 2 x 2-x-2 = 3. Where is g ( x ) = x 2-1 x < cos x-2 0 x < 3 + sin x x discontinuous? Justify your answer. 4. There are two points on the curve y = x 2 where the tangent line passes through (2 , 3). Find both. (16 pts). 5. Suppose lim x f ( x ) = 1, lim x g ( x ) = 0, lim x 1 f ( x ) = 2 and lim x 1 g ( x ) = 3. Find (3 points each): lim x ( g f )( x ) = lim x 1 ( f + g )( x-1) = lim x (( g-f ) f )( x ) = lim x 1 ( ( f ( x )) 2 + 1 ) = 6. Find lim x 1 x 2-x + 1-cos( x-1) x-1 . (12 pts). 7. According to the denition of the derivative, if f ( x ) = 1 x-1 then f ( x ) can be expressed as a limit. Write out this limit expression (3 pts) and evaluate (9 pts). 8. Find lim x x cos 1 x . Justify carefully. (12 pts)....
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## This note was uploaded on 07/17/2008 for the course MATH 151 taught by Professor Any during the Summer '08 term at Ohio State.

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test1sample - - , say so. (5 pts each): a. lim x 1 x 2-3 x...

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