Wiki-Quellcode von Lösung Differentialquotient A
Zuletzt geändert von akukin am 2025/11/22 20:20
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| author | version | line-number | content |
|---|---|---|---|
| 1 | (%class=abc%) | ||
| 2 | 1. | ||
| 3 | {{formula}} | ||
| 4 | \begin{align*} | ||
| 5 | f'(1) &= \lim_{x \to 1} \frac{f(x)- f(1)}{x - 1} \\ | ||
| 6 | &=\lim_{x \to 1} \frac{(x^2 + 3) - 4}{x - 1} \\ | ||
| 7 | &= \lim_{x \to 1} \frac{x^2 - 1}{x - 1} \\ | ||
| 8 | &= \lim_{x \to 1} \frac{(x - 1)(x + 1)}{x - 1} \\ | ||
| 9 | &= \lim_{x \to 1} (x + 1) \\ | ||
| 10 | &= 1 + 1 \\ | ||
| 11 | &= 2 | ||
| 12 | \end{align*} | ||
| 13 | {{/formula}} | ||
| 14 | 1. | ||
| 15 | {{formula}} | ||
| 16 | \begin{align*} | ||
| 17 | f'(1) &= \lim_{x \to 1} \frac{f(x)- f(1)}{x - 1} \\ | ||
| 18 | &= \lim_{x \to 1} \frac{3x^2 - 3}{x - 1} \\ | ||
| 19 | &= \lim_{x \to 1} \frac{3(x^2 - 1)}{x - 1} \\ | ||
| 20 | &= \lim_{x \to 1} \frac{3(x - 1)(x + 1)}{x - 1} \\ | ||
| 21 | &= \lim_{x \to 1} 3(x + 1) \\ | ||
| 22 | &= 3(1 + 1) \\ | ||
| 23 | &= 6 | ||
| 24 | \end{align*} | ||
| 25 | {{/formula}} |