test2_practice_2 - PRACTICE FOR TEST 2 1 If f(x = x 5 Find...

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Unformatted text preview: PRACTICE FOR TEST 2 1. If f ( x ) = √ x + 5 . Find f- 1 its domain and range. 2. Prove that d dx cot- 1 x =- 1 1 + x 2 3. Suppose a scoop of ice cream is placed on a wa e cone such that the wa e cone and scoop of ice cream have the same radius. Suppose that the height of the wa e cone is 5 . cm and that the ice cream scoop is melting so that the change in radius of the ice cream scoop is . 12 cm/sec. Assume that the melted liquid falls entirely into the wa e cone. Find the rate of increase of the height of melted liquid in the wa e cone when the height of the liquid is 2 cm. 4. Find the linearization at- 1 . f ( x ) = 1 √ 3+ x 5. Two cars start moving from the same point. One travels south at the rate of 60 mi/h and the other travels west at the rate of 25 mi/h. At what rate is the distance between the two cars increasing two hours later? 6. Use linear approximation, i.e. the tangent line, to approximate 3 √ 26 . 9 as follows: Let f ( x ) = 3 √ x . (a). Find the equation of the tangent line to....
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