Math16Apexam2 - bridge at a height of 32 feet above the...

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Math 16A: Practice problems for Midterm 2 Note: The midterm itself will not be this long. These are just some problems to get you ready. Problem 1. Find the derivatives of the following func- tions. (a) f ( x ) = ( x 2 + 1)( x - 5) (b) g ( x ) = x 2 +1 x - 5 (c) h ( x ) = sin( x 2 - x + 1) (d) k ( x ) = (cos( x ) + x ) 3 (e) r ( x ) = ( x 3 + x 2 ) 5 (f) s ( x ) = x 2 + x + 1 (g) t ( x ) = sin( x ) cos( x ) (h) u ( x ) = tan( x ) (i) v ( x ) = q x + x 2 (j) w ( x ) = sin( x ) · ( x 3 - cos( x )) 2. Using the definition of the derivative, find the deriva- tive of f ( x ) = 3 x . 3. Find the equation of the line that is tangent to the graph of f ( x ) = x 3 + x - 1 at the point (0 , - 1) . 1
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4. A spherical balloon is being inflated at a rate of 6 cubic inches per second. How quickly is the radius, r , growing when r = 3 inches? 5. A rock, thrown upward at 16 feet per second from a
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Unformatted text preview: bridge at a height of 32 feet above the water below, has a height (in feet) given by h ( t ) =-16 t 2 + 16 t + 32, where t is measured in seconds. (a) How long does it take the rock to hit the water? (b) What is the velocity of the rock as a function of time? (c) What is the velocity of the rock when it hits the water? (d) What is the average velocity of the rock while it is in the air? 6. Using the denition of the derivative, nd the deriva-tive of f ( x ) = x 2 . 7. What is the best linear approximation of the func-tion f ( x ) = x 2 + 1 near the point (0 , 1) ? 2...
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This note was uploaded on 06/23/2010 for the course MATH math16 taught by Professor Na during the Spring '10 term at UC Riverside.

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Math16Apexam2 - bridge at a height of 32 feet above the...

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