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- 7) The diameter of the base and the height of a closed right circular cylinder are measured,and measurements are known to have errors of at most 0.5 cm. If the diameter and height aretaken to be 4 cm and 8 cm, respectively, find bounds for the propagated error ina) the volume V of the cylinder, b) the surface area S of the cylinder.Use Simpson's 3/8 rule to compute the approximated solution where f (x) = 1/Cosx + 4 defined at the interval (1,4.5) and n = 7WHEN CAN YOU APPLY GREEN'S THEORM FOR Q BELOW
- Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5)A machinist is required to manufacture a circular metal disk with area 1000cm². If the machinist is allowed an error tolerance of ±9cm² in the area of the disk, how close to the ideal radius in part (1) must the machinist control the radius? What is the corresponding value of δ ?Determine the values of n and h required to approximate R02e2xsin(3x)dx towithin 10−4 using the composite trapezoid rule and composite Simpson’s rule.
- can we use L’Hôpital’s rule to solves this? May you teach me how?The brightness of a television picture tube can be evaluated by measuring the amount ofcurrent required to achieve a particular brightness level. A sample of 10 tubes results in x̅=317.2 and σx̅ = 15.7. Suppose that the design engineer claims that this tube will require atleast 300 microamps of current to produce the desired brightness level. Formulate and test anappropriate hypothesis to confirm this claim using α = 0.05.Use linear approximations to estimate the following. 1. sin 9/4