Reshebnik Ryabushko. Solved IDZ 12.2, Option 17
Replenishment date: 06.11.2018
Content: 17v-IDZ12.2.rar (58.92 KB)
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1. Find the region of convergence of the series. (1-3)
4. Expand the function f (x) in a Taylor series in a neighborhood of the specified point x0. Find the region of convergence of the resulting series to this function.
4.17. f (x) = 1 / x, x0 = −2
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.17. sin 10, α = 0,0001
6. Using the expansion of the integrand in a power series, calculate the specified definite integral with an accuracy of 0,001.
7. Find an expansion in a power series in powers of x of the solution to the differential equation (write down the first three nonzero terms of this expansion)
7.17. y ′ = x2 + xy + y2, y (0) = 0,5
8. Using the method of successive differentiation, find the first k terms of the power series expansion of the solution of the differential equation under the specified initial conditions.
8.17. y ′ ′ = y′2 + xy, y (0) = 4, y ′ (0) = −2, k = 5
4. Expand the function f (x) in a Taylor series in a neighborhood of the specified point x0. Find the region of convergence of the resulting series to this function.
4.17. f (x) = 1 / x, x0 = −2
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.17. sin 10, α = 0,0001
6. Using the expansion of the integrand in a power series, calculate the specified definite integral with an accuracy of 0,001.
7. Find an expansion in a power series in powers of x of the solution to the differential equation (write down the first three nonzero terms of this expansion)
7.17. y ′ = x2 + xy + y2, y (0) = 0,5
8. Using the method of successive differentiation, find the first k terms of the power series expansion of the solution of the differential equation under the specified initial conditions.
8.17. y ′ ′ = y′2 + xy, y (0) = 4, y ′ (0) = −2, k = 5
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.