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Unformatted text preview: + 1 = 0 prove that the equation a + a 1 x + a 2 x 2 + ..... + a n x n = 0 (1) has atleast one solution in the interval (0 , 1). Problem 5. Suppose that f is a continuous function on [0 , 2] such that f (0) = f (2). Show that there is a real number [1 , 2] with f ( ) = f ( -1). Problem 6. The axes of two right circular cylinders of radius a intersect at a right angle. Find the volume of the solid of intersection of the cylinders. Problem 7. Let f be a real valued function such that f,f ,f 00 are all continuous on [0 , 1]. Prove that the series X k =1 f ( 1 k ) is convergent if and only if f (0) = f (0) = 0....
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