<p>I have a final for the end of the term tomorrow, and I needed some help with this review question...</p>
<p>lim {[8(.5+h)^8] - [8(.5)^8]} / h. (the limit as h approaches 0).</p>
<p>Thanks!</p>
<p>oh yeah...the answer is 1/2...I just don't know how to get it...thanks again!</p>
<p>This limit is actually a derivative.</p>
<p>Factor out eight.</p>
<p>Then, you will see that the problem is asking you what the derivative of x ^ 8 is.</p>
<p>It's 8x ^ 7. Plug in one half for x to get 8 / 128.</p>
<p>Hey, that's not 1/2! Multiply (8 / 128) by 8 to get 64 / 128 = 1/2.</p>
<p>Fabrizio, you've got it all wrong.</p>
<p>lim [h-->0] f(x+h)-f(x)/h</p>
<p>He has:
lim [x-->0] 8(.5+h)^8 - 8(.5)^8/h</p>
<p>This makes f(x) have a numerical value, no x's involved</p>
<p>f(x) = 8(.5)^8</p>
<p>f'(x) = 64(.5)^7, which simplifies beautifully to the answer of .5</p>