Reshebnik Ryabushko. Solved IDZ 12.2, Option 15
Replenishment date: 06.11.2018
Content: 15v-IDZ12.2.rar (63.48 KB)
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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.
4.15. f (x) = xcos√x
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.15. 6√738, 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)
7.15. y ′ = ycosx + 2cosy, y (0) = 0
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.
8.15. y ′ ′ = y ′ / y - 1 / x, y (1) = 1, y ′ (1) = 0, k = 4
4. Expand the function f (x) in a Maclaurin series. Indicate the region of convergence of the obtained series to this function.
4.15. f (x) = xcos√x
5. Calculate the indicated value approximately with a given degree of accuracy α, using the power series expansion of the appropriately selected function
5.15. 6√738, 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)
7.15. y ′ = ycosx + 2cosy, y (0) = 0
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.
8.15. y ′ ′ = y ′ / y - 1 / x, y (1) = 1, y ′ (1) = 0, k = 4
Additional Information
The solution is executed in Microsoft Word 2003. The document with the IDZ solution is archived in the WinRar program.