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hoa [83]
3 years ago
5

Find and simplify the following for f(x) = x(19-x), assuming h+0 in (C).

Mathematics
1 answer:
alekssr [168]3 years ago
8 0

Answer:  see below

<u>Step-by-step explanation:</u>

f(x) = x(19 - x)

     = 19x - x²

A) f(x+h) = (x + h)[19 - (x + h)]

             = (x + h)(19 - x - h)

             = 19x - x² - 2xh + 19h - h²

B) f(x+h) - f(x) = (19x - x² - 2xh + 19h - h²) - (19x - x²)

                     = - 2xh + 19h - h²

                     = h(-2x + 19 - h)

C) [f(x+h) - f(x)]/h = [h(-2x + 19 - h)]/h

                           = -2x + 19 - h

As h → 0:           = -2x + 19

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