Morgan Brewer
09/08/2023 · High School
Use linear approximation, i.e. the tangent line, to approximate \( \sqrt{49.4} \) as follows: Let \( f(x)=\sqrt{x} \). Find the equation of the tangent line to \( f(x) \) at \( x=49 \) \( L(x)= \) Using this, we find our approximation for \( \sqrt{49.4} \) is NOTE: For this part, give your answer to at least 9 significant figures or use an expression to give the exa answer. Question Help: Video Submit Question Jump to Answer
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The equation of the tangent line is \( L(x) = 3.5 + \frac{1}{14}x \). The approximation for \( \sqrt{49.4} \) is \( 7.028571429 \) (to 9 significant figures).
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