The function f is defined by f(x)=x^(2)-sin(x). Use a calculator to write the equation of the line tangent to the graph of f when x=0.5. You should round all decimals to 3 places. Answer:

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The function  f is defined by  f(x)=x^(2)-sin(x). Use a calculator to write the equation of the line tangent to the graph of  f when  x=0.5. You should round all decimals to 3 places. Answer:

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Calculate Derivative: To find the equation of the tangent line to the graph of f(x) at x = 0.5, we need to calculate the derivative of f(x) to get the slope of the tangent line at that point. The derivative of f(x) = x^2 - sin(x) is f'(x) = 2x - cos(x).Evaluate Derivative at x=0.5: Now we need to evaluate the derivative at x = 0.5 to find the slope of the tangent line. f'(0.5) = 2(0.5) - cos(0.5). Using a calculator, we find that cos(0.5) is approximately 0.877, rounded to three decimal places. So, f'(0.5) ≈ 1 - 0.877 = 0.123.Find y-coordinate at x=0.5: Next, we need to find the y-coordinate of the point on the graph of f(x) at x = 0.5 to use it in the point-slope form of the equation of the tangent line. f(0.5) = (0.5)^2 - sin(0.5). Using a calculator, we find that sin(0.5) is approximately 0.479, rounded to three decimal places. So, f(0.5) ≈ 0.25 - 0.479 = -0.229.Use Point-Slope Form: With the slope of the tangent line and the point (0.5, -0.229), we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Plugging in our values, we get: y - (-0.229) = 0.123(x - 0.5).Simplify Equation: Simplify the equation to get it into the slope-intercept form y = mx + b. y + 0.229 = 0.123x - 0.0615. Now, we add 0.0615 to both sides to isolate y. y = 0.123x - 0.0615 + 0.229.Combine Constants: Finally, we combine the constants to get the final equation of the tangent line. y = 0.123x + 0.1675. This is the equation of the tangent line to the graph of f(x) at x = 0.5, rounded to three decimal places.

The function $f$ is defined by $f(x)=x^{2}-\sin (x)$ . Use a calculator to write the equation of the line tangent to the graph of $f$ when $x=0.5$ . You should round all decimals to $3$ places. $\newline$ Answer:

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The function $f$ is defined by $f(x)=x^{2}-\sin (x)$ . Use a calculator to write the equation of the line tangent to the graph of $f$ when $x=0.5$ . You should round all decimals to $3$ places. $\newline$ Answer: