Reed Salinas
07/19/2023 · Middle School

Use linear approximation, i.e. the tangent line, to approximate \( \sqrt{81.1} \) as follows: Let \( f(x)=\sqrt{x} \). Find the equation of the tangent line to \( f(x) \) at \( x=81 \) \( L(x)= \) Using this, we find our approximation for \( \sqrt{81.1} \) is NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exact answer. Ouestion Held: Video

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The equation of the tangent line is \( L(x) = 4.5 + \frac{1}{18}x \). The approximation for \( \sqrt{81.1} \) is approximately \( 9.005555556 \).

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