2.3a Lösning 8a - Versionshistorik

Taifun den 28 september 2014 kl. 20.26

2014-09-28T20:26:08Z

Taifun den 28 september 2014 kl. 20.25

2014-09-28T20:25:03Z

Taifun den 28 september 2014 kl. 20.18

2014-09-28T20:18:56Z

Taifun: Skapade sidan med ': $f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 =$ :: $\lim_{h \to 0}\,\...'$

2014-09-28T20:13:58Z

Skapade sidan med ':<math> f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = </math> ::<math> \lim_{h \to 0}\,\...'

Ny sida

:<math> f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = </math>

::<math> \lim_{h \to 0}\,\,{f(x+h) - f(x) \over h} = \lim_{h \to 0} {(x+h)^2 - x^2 \over h} = \lim_{h \to 0} {x^2 + 2\,x\,h + h^2 \, - \, x^2 \over h} = \lim_{h \to 0} {2\,x\,h + h^2 \over h} = </math>

::<math> = \lim_{h \to 0} {{\color{Red} h}\,(2\,x + h) \over {\color{Red} h}} = \lim_{h \to 0} \, (2\,x + h) = 2\,x </math>

@@ Rad 1: / Rad 1: @@
 :<math> \begin{array}{rcl} f(x+h) & = & (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = \\
-                                   & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = \\
+                                                                                                            \\
                                    & = & x^3 + 3\,x^2\,h + 3\,x\,h^2 + h^3
 \end{array}</math>

@@ Rad 1: / Rad 1: @@
 :<math> \begin{array}{rcl} f(x+h) & = & (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = \\
-                                   & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 =
+                                   & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = \\
 \end{array}</math>

@@ Rad 1: / Rad 1: @@
-:<math> f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = </math>
+:<math> \begin{array}{rcl} f(x+h) & = & (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = \\
+                                  & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 =
-::<math> \lim_{h \to 0}\,\,{f(x+h) - f(x) \over h} = \lim_{h \to 0} {(x+h)^2 - x^2 \over h} = \lim_{h \to 0} {x^2 + 2\,x\,h + h^2 \, - \, x^2 \over h} = \lim_{h \to 0} {2\,x\,h + h^2 \over h} = </math>
+\end{array}</math>
-−
-::<math> = \lim_{h \to 0} {{\color{Red} h}\,(2\,x + h) \over {\color{Red} h}} = \lim_{h \to 0} \, (2\,x + h) =  2\,x </math>

2.3a Lösning 8a - Versionshistorik

Taifun den 28 september 2014 kl. 20.26

Taifun den 28 september 2014 kl. 20.25

Taifun den 28 september 2014 kl. 20.18

Taifun: Skapade sidan med ': f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = :: \lim_{h \to 0}\,\...'

Taifun: Skapade sidan med ': $f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 =$ :: $\lim_{h \to 0}\,\...'$