Find the second Taylor polynomial T2(x) for the function f(x) = sin(x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-0.8, 0.8]. True or False? |f(x) - T2(x)| ≤ 0.8^3/3! for every x in I. True. False.
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Find the second Taylor polynomial T2(x) for the function f(x) = sin(x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-0.8, 0.8]. True or False? |f(x) - T2(x)| ≤ 0.8^3/3! for every x in I. True. False.
![Find the second Taylor polynomial T2(x) for the function f(x) = sin(x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-0.8, 0.8]. True or False? |f(x) - T2(x)| ≤ 0.8^3/3! for every x in I. True. False.](https://www.doubtrix.com/uploads/editor/5856011725QWKmCDeJCV.png)
![Find the second Taylor polynomial T2(x) for the function f(x) = e^x/4 based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval [-1, 1]. True or false: The Quadratic Approximation Error Bound indicates that |f(x) - T2(x)| ≤ 0.001672 for all x in I. True False](https://www.doubtrix.com/uploads/editor/1800175983gzlhCmvYQu.png)
![Find the Taylor polynomial T2(x) for the function f(x) = ln(1 + x) based at b = 0. T2(x) = Use the Quadratic Approximation Error Bound to bound the error |f(x) - T2(x)| on the interval I = [-1/3, 1/3]. Which of the following is true for all values of x in I? |f(x) - T2(x)| ≤ 0.0418 |f(x) - T2(x)| ≤ 0.2083 All of the above. None of the above.](https://www.doubtrix.com/uploads/editor/2180179679cRVQPXzcYq.jpeg)
![Find the second Taylor polynomial T2(x) for the function f(x) = cos(x) based at b = π/6. T2(x) = Let a be a positive real number and let J be the closed interval [π/6 - a, π/6 + a]. Use the Quadratic Approximation Error Bound to verify that |f(x) - T2(x)| ≤ a^3/3! for all x in J. Use this error bound to find a value of a so that |f(x) - T2(x)| ≤ 0.01 for all x in J. (Round your answer to six decimal places.) a =](https://www.doubtrix.com/uploads/editor/7211922884LPKkYMSdtJ.png)