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Zuletzt geändert von akukin am 2025/11/22 20:23
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1 (%class=abc%)
2 1.
3 {{formula}}
4 \begin{align*}
5 f'(x_0) &= \lim_{x \to x_0} \frac{f(x)- f(x_0)}{x - x_0} \\
6 &= \lim_{x \to x_0} \frac{(x^2 + 3) - (x_0^2 + 3)}{x - x_0} \\
7 &= \lim_{x \to x_0} \frac{x^2 - x_0^2}{x - x_0} \\
8 &= \lim_{x \to x_0} \frac{(x - x_0)(x + x_0)}{x - x_0} \\
9 &= \lim_{x \to x_0} (x + x_0) \\
10 &= x_0 + x_0 \\
11 &= 2x_0
12 \end{align*}
13 {{/formula}}
14 1.
15 {{formula}}
16 \begin{align*}
17 f'(x_0) &= \lim_{x \to x_0} \frac{f(x)- f(x_0)}{x - x_0}\\
18 &= \lim_{x \to x_0} \frac{3x^2 - 3x_0^2}{x - x_0} \\
19 &= \lim_{x \to x_0} \frac{3(x^2 - x_0^2)}{x - x_0} \\
20 &= \lim_{x \to x_0} \frac{3(x - x_0)(x + x_0)}{x - x_0} \\
21 &= \lim_{x \to x_0} 3(x + x_0) \\
22 &= 3(2x_0) \\
23 &= 6x_0
24 \end{align*}
25 {{/formula}}