Math Help, Question #5?

Find the following, where h doesn't = 0, for the function. Simplify your answer.

F(x) = x^ (1/2)

F(a+h) - F(a) / h

2 Answers

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  • 9 years ago
    Favorite Answer

    Hello,

    f(x) = √x

    [f(a+h) - f(a)] / h = [√(a + h) - √(a)] / h

       = [√(a + h) - √(a)] / [(a + h) - a] →→→ because h=(a+h)-a

       = [√(a + h) - √(a)] / { [√(a + h)]² - (√a)² } →→→ because x=(√x)²

       = [√(a + h) - √(a)] / { [√(a + h) - √a] × [√(a + h) - √a] } →→→ because x²-y²=(x+y)(x-y)

       = 1 / [√(a + h) - √a]

    Logically,

    Dragon.Jade :-)

  • 9 years ago

    {F(a+h) - F(a)}/ h = {sq rt(a+h) - sq rt(a)}/h = (1/h)*sq rt(a)*[sq rt{1+(h/a) -1}]

    ={sq rt(a)/h}[1 + (1/2)*(h/a)- (1/8)*(h/a)^2 + higher powers in the expansion - 1]

    = {1/(2a)}*sq rt(a)* [1 - h{1/4a + higher powers of h}

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