Question
Write the value of $\lim_\limits{\text{x}\rightarrow\text{c}}\frac{\text{f}(\text{x})-\text{f}(\text{c})}{\text{x}-\text{c}}$
$\frac{\text{d}}{\text{dx}}(\text{f}(\text{x}))=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{x}+\text{h}-\text{f}(\text{x}))}{\text{h}}$
Let,
$\text{h}=\text{x}-\text{c}$ and
$\text{f}(\text{x})=\text{c}$If
$\text{h}\rightarrow0$ then $\text{x}\rightarrow\text{c}$Therefore,
$\frac{\text{d}}{\text{dx}}(\text{c})=\lim_\limits{\text{x}\rightarrow\text{c}}\frac{\text{f}(\text{c}+\text{x}-\text{c})-\text{f}(\text{c})}{\text{x}-\text{c}}$
$=\lim_\limits{\text{x}\rightarrow\text{c}}\frac{\text{f}(\text{x})-\text{f}(\text{c})}{\text{x}-\text{c}}$
$=\text{f}'(\text{c})$
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Write the number of terms in the expansion of $(1-3\text{x}+3\text{x}^{2}-\text{x}^{3})^{8}.$
| Elementary events: | W1 | W2 | W3 | W4 | W5 | W6 | W7 |
| 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |