Question

Find second order expansion of f = 1/√x around x = 0.75, xo 1, xo 1.25. Calculate value of f function at x = 0.5, i) exact value, ii) the values obtained by the expansion functions which have found in the question. Comment about results.

Answer 1

The question involves calculating a second order Taylor series expansion of 1/√x around x = 0.75, x = 1, and x = 1.25 and evaluating the exact and approximated values at x = 0.5. This demonstrates the application and accuracy of Taylor series expansions in approximating functions.

Step-by-step explanation:

The student asked for a second order expansion of the function f(x) = 1/√x around different points and then to compute the value of the function at x = 0.5. The exact value can be easily calculated, but the expansion requires using a Taylor series expansion or a Maclaurin series expansion if the expansions are made around x = 1. Since the student asked for expansions around x = 0.75, x = 1, and x = 1.25, separate series are needed for each case, and each will yield different approximations when evaluated at x = 0.5. The comparison of the exact result with the approximations provides insight about the accuracy of Taylor series expansions near the expansion points.