Mat 201 final

# Mat 201 final - LaGuardia Community College FINAL EXAM MAT...

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LaGuardia Community College FINAL EXAM MAT 201 Print Name: Signature: ID #: Date: Directions: You have 60 minutes to answer the following questions. You must show all your work as neatly and clearly as possible and indicate the final answer clearly. You may NOT use a calculator. Problem Possible Points 1 16 2 6 3 12 4 6 5 4 6 10 7 4 8 8 9 14 Total 78

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Your signature: (1) Find the limit. (a) lim x 0 cos ( x + sin x ). (b) lim x 3 x 2 - 9 x 2 + 2 x - 3 . (2) Show that g ( x ) = x 2 - 9 x 2 - 4 is continuous on its domain.
Your signature: (3) Use the definition of the derivative to find f 0 ( x ) if f ( x ) = 4 - x 3 + x . (4) Find y 0 if y = tan x 1 + cos x . (5) Let f ( x ) = sec(1 + x 2 ), find f 0 ( x ).

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Unformatted text preview: (6) Find the linear approximation to f ( x ) = √ 25-x 2 near 3. Your signature: (7) Diﬀerentiate. (a) f ( x ) = ln(sin 2 x ) (b) g ( r ) = r 2 ln(2 r + 1) (c) H ( z ) = ln r 16-z 2 16 + z 2 Your signature: (8) Let f ( x ) = x 2 x 2 + 3 (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f . Your signature: (9) Let f ( t ) = t √ 4-t 2 . Find the absolute maximum and absolute minimum on the interval-1 ≤ t ≤ 2....
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• Spring '12
• Dr.D.A.Carter
• Calculus, #, Mathematical analysis, 60 minutes, LaGuardia Community College

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