Reshebnik Ryabushko. Solved IDZ 12.2, Option 13
Replenishment date: 06.11.2018
Content: 13v-IDZ12.2.rar (58.66 KB)
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Description
1. Find the region of convergence of the series. (1-3)
4. Expand the function f (x) in a Maclaurin series. Indicate the region of convergence of the obtained series to this function.
4.13. f (x) = 2 − x2
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.13. ln5, α = 0,001
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)
7.13. y ′ = e3x + 2xy2, y (0) = 1
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.
8.13. y ′ ′ = xyy ′, y (0) = y ′ (0) = 1, k = 6
4. Expand the function f (x) in a Maclaurin series. Indicate the region of convergence of the obtained series to this function.
4.13. f (x) = 2 − x2
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.13. ln5, α = 0,001
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)
7.13. y ′ = e3x + 2xy2, y (0) = 1
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.
8.13. y ′ ′ = xyy ′, y (0) = y ′ (0) = 1, k = 6
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.