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practicetest1

# practicetest1 - 9 A right cylinder is inscribed in a sphere...

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Practice problems 1. Sketch the graph of the derivative of the following functions: (page 142, problems 5-8) 2. Use Newton’s method to find the third approximation of a solution of x 3 + 2 x - 4 = 0 , if x 1 = 1 . (page 298, problem 5) 3. Approximate 3 30 to eight decimal places. (page 298, problem 11) 4. Calculate by definition the derivative of g ( x ) = 1 x 2 . (page 144, problem 28) 5. Find equations of both lines through (2 , - 3) tangent to the parabola y = x + x 2 .(page 156, problem 72) 6. Differentiate f ( x ) = sin x csc 2 x . 7. Differentiate: f ( x ) = sec x 1 + sec x . (page 174, problem 11) 8. Differentiate: ( a ) f ( x ) = sin( 1 + x 2 ) , ( b ) f ( x ) = sin(tan sin x ) . (page 182, problems 31 and 41)
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Unformatted text preview: 9. A right cylinder is inscribed in a sphere of radius r . Find the largest possible surface area of such a cylinder. (page 284, problem 27) 10. A piece of wire 10 m long is cut into two pieces. One piece is bent is into a square, the other into circle. How should the wire be cut such that the total area is: (a) maximal (b) minimum? (page 284, problem 32) 11. Find the equation of the line through (3 , 5) that cuts oﬀ the least possible surface area of from the ﬁrst quadrant. (page 285, problem 44)...
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