Evaluate difference quotient for given function?

👨🏻‍🏫 學術台數學

[匿名]

2012-05-27 8:01 pm

f(x) = 1/x, f(x)-f(a)/x-a
I tried but cannot get the answer -1/xa. I can get the denominator but niot the numerator. Can you help me?

回答 (2)

Ed I

2012-05-28 2:06 pm

✔ 最佳答案

[f(x) - f(a)]/(x - a) = [1/x - 1/a]/(x - a) = [a - x)/(ax)]/(x - a) = -1/ax

As x --> a, the difference quotient approaches -1/a^2.

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[匿名]

2012-05-28 3:21 am

[1/x - 1/a]/[x - a]
[a/(ax) - x/(ax)]/[x - a]
1/(ax)*[a - x]/[x - a]
1/(ax)*(-1)
-1/(ax)

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