Question
x at x = 1
✓
Answer
We have,
$\text{f(x)}=\text{x}$
$\because\text{f}'\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(a+h)}-\text{f(a)}}{\text{h}}$
$\therefore\text{f}'\text{(1)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(1+h)}-\text{f(1)}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\text{1+h}-1}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0} 1$
$\therefore\text{f}'(1)=1$
$\text{f(x)}=\text{x}$
$\because\text{f}'\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(a+h)}-\text{f(a)}}{\text{h}}$
$\therefore\text{f}'\text{(1)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(1+h)}-\text{f(1)}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\text{1+h}-1}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0} 1$
$\therefore\text{f}'(1)=1$
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