3. In this problem, round the derivative to four decimal places. Find the straight line (tangent) approximation to $y = f(x) = \sqrt{x}$ at $x=1000$. $\frac{dy}{dx}|_{x=1000} = \frac{1}{2\sqrt{x}}|_{x=1000} = \frac{1}{2\sqrt{1000}} \approx 0.0158$ Straight Line approximations is: $y - \sqrt{1000} \approx y'(1000)(x - 1000) \implies y \approx 0.0158(x - 1000) + \sqrt{1000}$ Use that straight line above - NOT YOUR CALCULATOR - to approximate the following to 4 decimal places. Use the straight line above to find $\sqrt{1002}$, $\sqrt{1005}$, $\sqrt{1010}$, $\sqrt{1020}$ (answers to four decimal places). Put answers in chart below along with the values using the calculator to find the values to four decimal places. Value of x 1002 1005 1010 1020 Straight Line Approximation of $\sqrt{x}$ (4 decimal places) Value of $\sqrt{x}$ from Calculator to 4 decimal places
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The derivative of y = f(x) = x is simply 1, as the derivative of x with respect to x is 1. Show moreβ¦
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