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Unformatted text preview: Solution : Two resistors R 2 are in parallel and can be replaced by one resistor R 2 / 2. The total current owing through the circuit is I = E R 1 + R 2 / 2 1 R C R R 2 2 1 The voltage on the parallel resistors and on the capacitor is V = I R 2 2 = R 2 2 R 1 + R 2 E This give the capacitor charge Q = CV = R 2 C E 2 R 1 + R 2 3 Problem 3 Consider a function f ( x ) = x 2 e x . Find the positions of the extremum points. Sketch the graph of the function. Solution : First, we have f ( x ) = 2 xe x + x 2 e x = x ( x + 2) e x The equation f ( x ) = 0 has two solutions x 1 = 0 and x 2 =-2. The graph of the function looks as-2 2...
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