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2.3a Lösning 10 - Versionshistorik
2026-11-05T11:39:50Z
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Taifun den 28 september 2014 kl. 19.59
2014-09-28T19:59:50Z
<p></p>
<p><b>Ny sida</b></p><div>:<math> \begin{array}{rcl} f(x+h) - f(x) & = & {1 \over x+h} - {1 \over x} = {x \over x\,(x+h)} - {x+h \over x\,(x+h)} = {x - (x+h) \over x\,(x+h)} = {x - x - h \over x\,(x+h)} = \\<br />
\\<br />
& = & {- h \over x\,(x+h)} <br />
\end{array}</math><br />
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:<math> {f(x+h) - f(x) \over h} = {- h/h \over x\,(x+h)}= {- 1 \over x\,(x+h)} </math><br />
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:<math> \lim_{h \to 0} {f(x+h) - f(x) \over h} = \lim_{h \to 0} \; {- 1 \over x\,(x+h)} = {- 1 \over x\,(x+0)} = - \, {1 \over x^2} </math></div>
Taifun