Consider the function f(x) := v/x= x1/2. 6. (a) Give the Taylor polynomial P(x) of degree 5 about a1 of this function (b) Give the nested representation of the polynomial Qs()Ps((t)) where t -1 (...
a. Use the given Taylor polynomial p, to approximate the given quantity b. Compute the absolute error in the approximation assuming the exact value is given by a calculator Approximate e-004 using f(x) = -* and p(x) = 1 -x+ a. Using the Taylor polynomialpy.c-004 (Do not round until the final answer. Then round to four decimal places as needed.) b. absolute error (Uso scientific notation. Use the multiplication symbol in the math palette as needed. Round to two decimal...
2. Compute the linear Taylor polynomial for the function exp (x + x4 f (x) at a = 0 and give a reasonable estimate for the error for l 0.01. 2. Compute the linear Taylor polynomial for the function exp (x + x4 f (x) at a = 0 and give a reasonable estimate for the error for l 0.01.
let a = 35 Please show work! 2. Select a distinctive positive integer a with a > 10 that is not a perfect cube a) Use a third degree Taylor Polynomial to approximate v b) Compute an upper bound for the error made in the approximation in (a) (c) Using the output of a calculator or computer as the "exact" value of Va, compute the "exact" error in the approximation in (a). 2. Select a distinctive positive integer a with...
The nth-order Taylor polynomial for a function f(x) using the h notation is given as: Pa (x + h) = f(x) + f'(a)h + salt) 12 + () +...+ m (s) n." The remainder of the above nth-order Taylor polynomial is defined as: R( +h) = f(n+1)(C) +1 " hn+1, where c is in between x and c+h (n+1)! A student is using 4 terms in the Taylor series of f(x) = 1/x to approximate f(0.7) around x = 1....
2. a) Find Ts(x), the third degree Taylor polynomial about x -0, for the function e2 b) Find a bound for the error in the interval [0, 1/2] 3. The following data is If all third order differences (not divided differences) are 2, determine the coefficient of x in P(x). prepared for a polynomial P of unknown degree P(x) 2 1 4 I need help with both. Thank you.
1. Consider the polynonial Pl (z) of degree 4 interpolating the function f(x) sin(x) on the interval n/4,4 at the equidistant points r--r/4, xi =-r/8, x2 = 0, 3 π/8, and x4 = π/4. Estimate the maximum of the interpolation absolute error for x E [-r/4, π/4 , ie, give an upper bound for this absolute error maxsin(x) P(x) s? Remark: you are not asked to give the interpolation polynomial P(r). 1. Consider the polynonial Pl (z) of degree 4...
Complete all, especially part c and d (a) Glive the second-order Taylor polynomial T2 ( for the function () about a 16. 4+((X-16)/8)-(1/512) (X-16M2 b) Use Taylor's Theorem to give the Error Term E2(-f()T2) as a function of z and some z between 16 and az (((3/8) Z(-5/2)) (X-16) 3)/6 c) Estimate the domain of values z for which the error E2 () is less than 0.01. Enter a value p for which E2 ()I 0.01 for all 16 16+p,...
Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2) and P2(2) estimate the absolute error IIn(2) - P2(2)] s? Quiz 5. Due Wednesday May 22, 2019. zo- e 1,e, 2-. Give the representation Consider interpolating the function In(x (without developing and 'simplifying in al) of the interpolation polynomial Pa(z) expressed by Without calculating In(2)...
Consider the following function. /(x)=x-5, a= 1, n= 2, 0.8SXS 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a T2(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation x) ~ Tn(x) when x lies in the given interval. (Round your answer to six decimal places.) (c) Check your result in part (b) by graphing Rn(x) 0.6 0.4 0.2 0.6 0.4 0.2 0.9 0.9 1.2 -0.2 -0.4 -0.6 -0.2 -0.4 -0.6...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...