Use linear approximation, i.e. the tangent line, to approximate $\displaystyle {10.1}^{{2}}$ as follows:
Let $\displaystyle {f{{\left({x}\right)}}}={x}^{{2}}$ and find the equation of the tangent line to $\displaystyle {f{{\left({x}\right)}}}$ at $\displaystyle {x}={10}$.

Using this, find your approximation for $\displaystyle {10.1}^{{2}}$


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