(a) find t4(x), the 4th degree taylor polynomial for f(x) = sin x centered at a = π/6. (b) use taylor’s inequality to estimate the accuracy of the approximation f(x) ≈ t4(x) when 0 ≤ x ≤ π/3. in other words, what is the biggest error we could have if we were to use t4(x) in place of f(x) = sin x on the interval [0, π/3]?

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec