The approximate value of $\cot ^{-1}(1 \cdot 001)$ is
The approximate value of $\cot ^{-1}(1 \cdot 001)$ is
$\frac{\pi}{4}-0 \cdot 0005$
$\frac{\pi}{4}+0 \cdot 005$
$\frac{\pi}{4}+0 \cdot 0005$
$\frac{\pi}{4}-0 \cdot 005$
Solution
Let $f(x)=\cos ^{-1} x \Rightarrow f^{\prime}(x)=\frac{-1}{1+x^{2}}$
Let, $\mathrm{a}=1, \mathrm{~h}=0.001$
Now $\mathrm{f}(\mathrm{a})=\cot ^{-1} 1=\frac{\pi}{4}$ and $\mathrm{f}^{\prime}(\mathrm{a})=\frac{-1}{1+1}=-\frac{1}{2}$
We know that, $f(a+h) \doteqdot f(a)+h f^{\prime}(a)$
$=\frac{\pi}{4}+(0.001)\left(-\frac{1}{2}\right)=\frac{\pi}{4}-0.0005$