Finding difference quotient
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The Difference Quotient Formula is a part of the definition of a function derivative. One can get derivative of a function by applying Limit h tends to zero i.e., h ⇢ 0 on difference
f (3.1) = (3.1) 2 − 2×3.1 + 1 = 4.41. And the Difference Quotient is: f (3.1) − f (3) 0.1 = 4.41 − 4 0.1 = 0.41 0.1 = 4.1. As Δx heads towards 0, the value of the slope heads towards the true slope at x.
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Solution: Using the difference quotient formula, the difference quotient of f (x) is, [ f (x + h) - f (x) ] / h. = [ ln (x + h) - ln x ] / h. = ln [ (x + h) / x ] / h (because by quotient property of logarithms, ln m - ln n = ln (m / n)) Answer: The difference
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