Find the linearization of the function below at x = π/3.?


Your answer should be a linear function of x where the coefficients are accurate to at least two decimal places. You can enter π in your answer as "pi" (without the quotes).

I am not able to figure out how to find the answer. I tried couple times but it is showing incorrect.Please show the answer as well because I was not able to get the correct answer last time either. Please help me.. Thank you.

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  1. take y' = dy / dx
    y' = [x cos x -sin x]/x^2
    at x = pi/3
    y' = [ pi/3 cos pi/3 - sin pi/3 ] / (pi^2/9)

    =[ pi/3 *1/2 - sqrt3 /2 ]/(pi^2/9)

    = [ pi/6 - 3 sqrt 3 /6 ] 9/pi^2

    = 1.5(pi-3 sqrt 3)/pi^2
    that is m in y = mx+b
    to get b once you calculate m

    at x = pi/3
    y = sin (pi/3) / (pi/3)
    y = (3/pi) sqrt3 / 2
    1.5 sqrt3/ pi = m (pi/3) + b
    solve for b

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