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Unformatted text preview: is that?) Martha, an escaping prisoner, is running along the wall trying to keep just ahead of the beam of light. At the moment when the searchlight angle is 60 degrees, how fast does she have to run? Problem 5. (15: 5, 10) x a) What value for the constant c will make the function e 1 + cx approximately constant, for values of x near 0? (Show work.) dx b) Find the solution x ( t ) to the dierential equation = 2 t 1 x 2 dt which also satises the condition x (0) = 1. Problem 6. (15: 8,7) a) Use the Mean-value Theorem to show that ln(1 + x ) < x, if x > 0. (You do not have to state the theorem.) b) Let c be any constant. Show that the function f ( x ) = x 3 + x + c cannot have two zeros. (Use the Mean-value theorem, or some other argument.)...
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