Question

Use linear approximation, i.e. the tangent line, to approximate √3 / 27.1 as follows: Let f(x)= x. Find the equation of the tangent line to f(x) at x=27 L(x)= Using this, we find our approximation for 27.1 is

Answer 1

To approximate the value of √3 / 27.1 using linear approximation, we find the equation of the tangent line to the function f(x) = x at x = 27 and substitute 27.1 into the equation to get our approximation of 1.1.

Step-by-step explanation:

To approximate the value of √3 / 27.1 using linear approximation, we first need to find the equation of the tangent line to the function f(x) = x at x = 27. To do this, we find the slope of the tangent line by taking the derivative of f(x), which is 1. Since the derivative gives us the slope of the tangent line at any given point, the equation of the tangent line is y = 1(x - 27) + f(27). Simplifying this equation, we get y = x - 26.

Next, we can use this equation to approximate √3 / 27.1 by substituting 27.1 into the equation of the tangent line. Our approximation is therefore 27.1 - 26 = 1.1.