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Unformatted text preview: greatest volume that can be inscribed in a given right circular cone of height 1 meter and radius 1 meter. 6. a) (10 points) Show that the equation ln x-x + 2 = 0 has at least two solutions. b) (10 points) Show that it has exactly two solutions. 7. (20 points) Find the linear approximation to f ( x ) = 1 (1 + x ) 4 at a = 0, and use it to approximate 1 1 . 1 4 . 8. (15 points) A cube is increasing in volume at a rate of 10 cm 3 /sec . Find the rate of change of the surface area of the cube when one edge has length 2cm. 9. Let f ( x ) = x 2 cot x x 6 = 0; x = 0 . a) (10 points) Show that f is continuous at x = 0. b) (10 points) Show that f dierentiable at x = 0....
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