##### Find f(a), f(a + h), and the difference quotient f(a + h) − f(a) h , where h

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1.    f(x) =

 2 x + 5

f(a + h) − f(a)/h=

2.       f(x) =

x/x + 2

f(a + h) − f(a)/h=

3.       f(x) = 3 − 2x + 4x2

f(a + h) − f(a)/h=

Feb 7th, 2015

f(x) = 2/(x+5)

f(a+h) = 2/(a+h+5)
f(a) = 2/(a+5)

[f(a+h) - f(a)]/h = [2/(a+h+5) - 2/(a+5)]/h = [2(a+5) - 2(a+h+5)]/h(a+5)(a+h+5) = -2h/ h(a+5)(a+h+5)
= -1/(a+5)(a+h+5)

f(x) =
x/x + 2

f(a+h) = (a+h)/(a+h+2)
f(a) = a/(a+2)

[f(a+h) - f(a)]/h= [(a+h)/(a+h+2) - a/(a+2)]/h = [(a+h)(a+2) - a(a+h+2)]/h(a+h)(a+h+2)
= [a^2 + 2a + ah +2h - a^2 - ah -2a]/h(a+h)(a+h+2)
= 2h/h(a+h)(a+h+2) = 2/(a+h)(a+h+2)

f(x) = 3 − 2x + 4x^2

f(a+h) = 3 - 2(a+h) + 4(a+h)^2 = 3 - 2a -2h +4a^2+8ah+4h^2
f(a) = 3 - 2a + 4a^2

[f(a+h) - f(a)]/h = [3 - 2a -2h +4a^2+8ah+4h^2 - (3 - 2a + 4a^2)]/h
=[3 - 2a -2h +4a^2+8ah+4h^2 - 3 + 2a - 4a^2)]/h
= [-2h + 8ah + 4h^2]/h

= 4h + 8a -2

Feb 7th, 2015

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Feb 7th, 2015
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Feb 7th, 2015
Dec 9th, 2016
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