ptest2A - / 2 a meter in radius. Estimate the change in...

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Name: Practice Test 2A for MTH 151K 1. Evaluate y : (a) y = sin 2 (ln x ). (b) y = ln t t 2 . (c) y = (sin x ) x . (d) y = 3 r ( x 3 + 1)( x + 1) 3 . 2. Find y : (a) y = x 2 arctan x . (b) y = arcsin( x 3 ). (c) y = arctan x 1+ x 2 . 3. Prove the following di±erentiation formula: d dx [arctan x ] = 1 1 + x 2 . 4. A 10-foot-long ladder leans against a vertical wall. The base of the ladder begins to slide away from the wall at the rate of 2 feet per second. How quickly is the top of the ladder sliding down the wall at the instant when the base of the ladder is 6 feet away from the wall? 5. A cylinder initially measures 2 meters in height and 1
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Unformatted text preview: / 2 a meter in radius. Estimate the change in volume if the radius of the cylinder is increased to 9 / 16 of a meter. 6. Find the maximum and minimum values of the function on the given interval: f ( x ) = x 3-x ; [-1 , 1] . 7. Find the maximum and minimum values of the function on the given interval: f ( x ) = x 1 + x 2 ; [0 , 3] . 8. Show that the following equation has exactly one solution: 2 x 3 + 3 x 2 + 6 x + 2 = 0 ....
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