a) Find the simplified form of the difference quotient for the function f(x) = 5/x. b) Complete the following table: |x | h | (f(x+h) - f(x))/h | |---|---|---------------------| |3 | 3 | 3 | |2 | 1 | 0.1 | |0.1 | 0.01 | 0.001 | b) Complete the following table: |f(x+h) - f(x) | h | |--------------|---| |3 | 2 | |3 | 1 | |3 | 0.1 | |3 | 0.01 |
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The difference quotient is given by: (f(x+h) - f(x))/h Substitute f(x) = 5/x into the formula: (f(x+h) - f(x))/h = (5/(x+h) - 5/x)/h To simplify, find a common denominator: = (5x - 5(x+h))/(x(x+h))/h = (5x - 5x - 5h)/(x(x+h))/h = -5h/(x(x+h))/h = Show more…
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