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# 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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- Dragon.JadeLv 79 years agoFavorite 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 :-)

- Let'squestionLv 79 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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