Description
Find f(a), f(a + h), and the difference quotient f(a + h) − f(a)/h
, where h ≠ 0.
f(x) = x/x + 2
f(a) =
Correct: Your answer is correct.
f(a + h) =
Correct: Your answer is correct.
????? HELP f(a + h) − f(a)/h =
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Explanation & Answer
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)
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