Thread: Evaluating Limits Analyticall
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Old October 2nd, 2007, 08:38 AM
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Originally Posted by Amadeus View Post
Thank you very much! I understand (for the most part)

Although I got stuck on this one...

Below, find lim f(x+h) - f(x) / h
----------- (x->0)

f(x) = 4/x

I tried it and got the first step as:

(4/x+h) - (4/x) / h

At this step, I'm pretty sure I'm on the wrong track but I multiplied both top & bottom by (4/x + h) + (4/x)

Again, it turns out weird and I'm lost...
Your limit has a typo. It should be as h goes to 0.

This one simply has a lot of algebra involved:
\lim_{h \to 0}\frac{\frac{4}{x + h} - \frac{4}{x}}{h}

Subtract the fractions:
= \lim_{h \to 0}\frac{\frac{4x}{x(x + h)} - \frac{4(x + h)}{x(x + h)}}{h}

= \lim_{h \to 0}\frac{4x - 4(x +h)}{hx(x + h)}

= \lim_{h \to 0}\frac{-4h}{hx(x + h)}

= \lim_{h \to 0}\frac{-4}{x(x + h)}

Now take the limit:
= \frac{-4}{x^2}

-Dan
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