Homework Help: calculus

Posted by john on Thursday, October 14, 2010 at 8:53pm.

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

y=sin(x)/x

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.

calculus - Damon, Thursday, October 14, 2010 at 9:28pm
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
so
1.5 sqrt3/ pi = m (pi/3) + b
solve for b

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