# 8th - 6 Find a function f such that f x = x 3 and the line...

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Math 119 Recitation 8 November 6, 2006 1. Find the dimensions of the isoceles triangle of largest area that can be inscribed in a circle of radius r . 2. A right circular cylinder is inscribed in a sphere of radius r . Find the largest possible surface area of such cylinder. 3. At which points on the curve y = 1 + 40 x 3 - 3 x 5 does the tangent line have the largest slope? 4. Find the point on the hyperbola xy = 8 that is closest to the point (3 , 0) 5. Use Newton’s method with initial point x 1 = 1 to ﬁnd x 3 , the third approximation to the root of the equation x 3 - x 2 - 1 = 0.
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Unformatted text preview: 6. Find a function f such that f ( x ) = x 3 and the line x + y = 0 is tangent to the graph of f . 7. A paticle is moving with acceleration a ( t ) = cos t + sin t . Given that s (0) = 0 and v (0) = 5, ﬁnd the position of the particle. 8. Determine a region whose area is equal to lim n →∞ ∑ n i =1 2 n (5 + 2 i n ) 10 . 9. Find an expression for the area under the curve y = x 3 from 0 to 1 as a limit and use the formula 1 + 2 3 + 3 3 + · · · + n 3 = [ n ( n +1) 2 ] 2 to evaluate the limit. 1...
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## This note was uploaded on 04/30/2010 for the course MATHEMATIC MATH 119 taught by Professor Tor during the Spring '10 term at Middle East Technical University.

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