For better approximation choose one of the appropriate Newton's interpolating polynomials, Forward Difference,Backward Difference or Stirling's Formula, of order 3 to calculate y for x = 0.63 for the given data. (Use four decimals.)Xy010.21.22140.40.61.4918 1.82210.82.225512.7275

The value of table for x and y:x00.20.40.60.81y11.22141.49181.82212.22552.7275

Answered: For better approximation choose one of…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 52E

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The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.
From the given data,identify f(4) using a Lagrance and Newton's polynomial (2,10),(3,15),(5,25),(8,40)
A) Calculate the sixth degree Mac Laurin polynomial for e^-x2 and obtain an approximate value for the fraction 1÷√e. B) Calculate the following definite integral:
Since YouTube first became available to the public in mid-2005, the rate at which video has been uploaded to the site can be approximated by v(t) = 1.1t2 − 2.6t + 2.3 million hours of video per year (0 ≤ t ≤ 9), where t is time in years since the start of June 2005.† (a) Find an expression for the total number of hours V(t) of video at time t (starting from zero hours of video at t = 0). (Round your coefficients to four decimal places.) V(t) = (b) Use the answer to part (a) to estimate the total number of hours of video uploaded by the start of 2011. (Round your answer to the nearest million hours of video.) million hours of video
Consider the following function. f(x) = ln(1 + 2x), a = 2, n = 3, 1.6 ≤ x ≤ 2.4 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) |R3(x)| ≤ (c) Check your result in part (b) by graphing |Rn(x)|.
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = ln(x + 1), approximate f(0.5). at the indicated value of x to be less than 0.001, f(x) = 1/(x + 1), approximate f(0.2)
Consider the following function. f(x) = e4x2, a = 0, n = 3, 0 ≤ x ≤ 0.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = ______ (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ Tn(x) when x lies in the given interval. (Round your answer to five decimal places.) |R3(x)| ≤ ______
The function f(x) has its fifth derivative continuous on (−∞,∞). (a) If |f(5)| < 6 on the interval [2.9,3.1], to how many decimal places does the fourth Taylor polynomial T4(x) of f(x) centered at 3 approximate f(x) on this interval?
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Find the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2].
Suppose that an oil spill in a lake covers a circular area and that the radius of the circle is increasing according to the formula r = f(t) = 12 + t1.65, where t represents the number of hours since the spill was first observed and the radius r is measured in meters. (Thus when the spill was first discovered, t = 0 hr, and the initial radius was r = f(0) = 12 + 01.65 = 12 m.) (a) Let A(r) = πr2, as in Example 5. Compute a table of values for the composite function A ∘ f with t running from 0 to 5 in increments of 0.5. (Round each output to the nearest integer.) Then use the table to answer the questions that follow in parts (b) through (d). t 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 A (b) After one hour, what is the area of the spill (rounded to the nearest 10 m2)? m2(c) Initially, what was the area of the spill (when t = 0)? m2Approximately how many hours does it take for this area to double? hr(d) Compute the average…

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For better approximation choose one of the appropriate Newton's interpolating polynomials, Forward Difference, Backward Difference or Stirling's Formula, of order 3 to calculate y for x = 0.63 for the given data. (Use four decimals.) X y 0 1 0.2 1.2214 0.4 0.6 0.8 1 1.4918 1.8221 2.2255 2.7275