Linear Approximation

What:

In Calculus, when something is hard to calculate, we may try to get an approximation. The general form is as follows: $f(x)\approx L(x)=f(a)+f^{\prime }(a)(x-a)$

Example:

Take $\sqrt{9.2}$ → using $f(x)=\sqrt{x}$ and $f^{\prime }(x)=\frac{1}{2\sqrt{x}}$ and $a=9$. Thus $\sqrt{9.2}\approx 3+\frac{1}{6}\cdot 0.2=3.033\dots$