F 1 8 f 1 8 4 10 pts write down each of the following

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f 1 (8) ( f 1 ) (8) ______________________________________________________________________ 4. (10 pts.) Write down each of the following derivatives. [2 pts/part.] (a) d [tan 1 ] dx ( x ) (b) d [sin 1 ] dx ( x ) (c) d [ csc 1 ] dx ( x ) (d) d [cos 1 ] dx ( x ) (e) d [cot 1 ] dx ( x )
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TEST3/MAC2311 Page 3 of 5 ______________________________________________________________________ 5. (10 pts.) Fill in the blanks appropriately. [DEFINITIONS!!!] (a) A function f has a relative maximum at x 0 if there is an open interval containing x 0 on which for each x in both the interval and the domain of f . (b) A function f is concave down on an interval ( a , b ) if the derivative of f is on ( a , b ). (c) A function f is concave up on an interval ( a , b ) if the derivative of f is on ( a , b ). (d) A function f is decreasing on an interval ( a , b ) if whenever a < x 1 < x 2 < b . (e) A function f is increasing on an interval ( a , b ) if whenever a < x 1 < x 2 < b . ______________________________________________________________________ 6. (5 pts.) Find the following limit by interpreting the expression as an appropriate derivative. lim w 2 3 sec 1 ( w ) π w 2 ______________________________________________________________________ 7. (5 pts.) Suppose the side of a square is measured to be 10 inches with a possible error of ± 1/32 inch. Estimate the error in the computed area of the square by using differentials. [You may leave your result as a fraction. You do not have to convert to decimal form.]
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