Unformatted text preview: Let M ( t ) denote the maximum value of | t-x | /x as x varies from a to b . (a) Prove that this maximum occurs at one of the endpoints of [ a,b ] (b) Prove that M ( t ) is smallest when t is such that 1 t = 1 2 ( 1 a + 1 b ) 6. Let f = 1 6 x 2 + 1 12 cos 2 x . Determine the intervals in which f is monotonic (i.e. increasing or decreasing) and intervals in which f is monotonic. 7. Show that x 2 = x sin x + cos x for exactly two real values of x . 8. A particle is constrained to move along a parabola whose equation is y = x 2 . (a) At what point on the curve are the abscissa and ordinate changing at the same rate? (b) Find this rate if the motion is such that at time t we have x = sin t and y = sin 2 t . 1...
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- Spring '10
- Electrical Engineering, Order theory, Monotonic function, ln ln, University of Engineering and Technology Lahore Department of Electrical Engineering