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Math+19A+-+Review+2+-+Fall+11

# Math+19A+-+Review+2+-+Fall+11 - Math 19A Review 2 Fall 11 1...

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Math 19A - Review 2 - Fall 11 1.) Differentiate. (a.) f ( x ) = 3 x 2 + 2 x + 1 (j.) h ( s ) = 3 s 4 +5 (b.) g ( x ) = 1 ( x 4 + 3) 5 (k.) y = 1 + ln( x ) 1 - ln( x ) (c.) h ( x ) = 5 x - 1 3 x 2 + 2 (l.) x ( z ) = 3 z cosh( z 3 ) (d.) y = 3 x - 1 ( x 3 + 1) 2 (m.) φ ( t ) = tan - 1 ( e t 2 ) (e.) G ( x ) = tan( x ) x 2 (n.) g ( θ ) = ln(sec( θ ) + tan( θ )) (f.) s ( θ ) = sin 2 (cos( θ )) (o.) F ( x ) = tan - 1 ( x 1 + x 2 ) (g.) f ( x ) = sec 3 ( 1 + x 2 ) (p.) h ( x ) = x x (h.) θ ( t ) = e 5 t cos 2 ( t 3 ) (q.) g ( x ) = x cos( x ) (i.) y = e x sec(2 x ) (r.) f ( x ) = [ln( x )] x 2.) Let f ( x ) = x 2 x + 1 . Find f 000 ( x ). 3.) Use implicit differentiation to find dy/dx . (a.) x 2 + xy - y 2 = 4 (b.) 1 + x = sin( xy 2 ) (c.) y 5 + x 2 y 3 = 1 + x 4 y (d.) y sin( x 2 ) = x sin( y 2 )

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4.) Suppose s ( t ) = t 3 - 18 t 2 +105 t , 0 t 10, gives the position of a particle moving in one dimension as a function of time where s is measured in feet and t is measured in seconds. What is the total distance traveled by the particle during the 10 second time interval? When is the particle speeding up? When is it slowing down? 5.) Use an appropriate linearization to find a rational approximation of 3 728.
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