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Algebra

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I don't understand how to do the folliwing problems.

Find and simplify the difference quotient f(x+h) -f(x)/h, h cannot equal 0 for the given formula.

1. f(x)=5x^2

options: a. 5, b.5(2x+h), c. 10/h +x+5h, d. 5(2x^2+2xh+h^2)/h

2. f(x)=x^2+3x+9
options: a. 2x+h+9, b.1, c.2x^2+2x+2xh+h^2+h+18/h, d. 2x+h+3

  • Algebra - ,

    Here is how to do #1. #2 is the same.
    f(x+h) = 5 (x+h)^2 = 5x^2 + 10 xh + 5h^2
    f(x+h) - f(x) = 10xh + 5h^2
    [f(x+h) - f(x)]/h = 10 x + 5h = 5x (2+h)
    This is answewr # (b)
    As h -> 0, the ratio approaches 10 x

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