Show that the function represented by the power series is a solution of the differential equation.y=∑limits^( ∞ )_(n=0)(-1)^n(x^(2n))(4^n(n!)^2), x^2y''+xy'+x^2y=0 相关知识点: 试题来源: 解析 We first find the first and second derivatives of yy'=∑limits^( ∞ )_...
Power series is really fun to deal with. In this problem, you are to find the function represented by the given series. Yes, it could be tough if you are not familiar with some of the common power series expansions. But, do not worry if you do not know any because...
Power series representations are also useful in approximating the value of a functionf(x)ifxis very small or very large. In physics, sine and cosine functions with power series representations given by sinx=∑n=0∞(−1)n(2n+1)!x2n+1=x−13!x3+15!x5...
The function in Figure 9-17 determines the number represented in binary by a bit-vector value. The algorithm scans the bit vector from the most-significant end. For each bit, it multiplies the previously accumulated value by two and then adds in the integer value of the bit. The accumulated...
Ex: The UTC time represented when the offset is applied... Example of @"^[a-zA-Z0-9 ._-:\?]+$" Pattern Example of Lazy Loading in asp.net via c# Example of using Nlog in VB.NET excel = New Excel.Application: "Microsoft.Office.Interop.Excel.dll" Excel cannot open the file sampl...
For all the arguments, cash you pay out, such as deposits to savings, is represented by negative numbers. Cash you receive, such as dividend checks, is represented by positive numbers. Example Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet...
Of course, here dfdxx will be represented by a 1 × n matrix since, just like the function we are linearizing, it goes from ℝn to ℝ. However: fx+δx=x+δxT.Q⋅x+δx=xT⋅Q⋅x+xT⋅Q⋅δx+δxT⋅Q⋅x+δxT⋅Q⋅δx=xT⋅Q⋅x+2xT⋅Q⋅δx+o(∥δ...
When a general-purpose counter is configured to output a pulse, the length of time that the pulse is active is represented by the value in the counter's register. The combination of this value and the rate that the counter is counting (set by the counter's base clock)...
function is represented as g−1(x) and we have the infinite power series for this function from the table of Taylor series, then we'll compute the infinite series for a function that has double angle such as g−1(2x) by replacement of each variable of the...
This is written as δ(x), where x represents space coordinates or time, and is represented as a generalized function by Fig. 6.5 (see Fourier Analysis and Generalised Functions (Lighthill, 1964), listed in the Bibliography). It has the following properties:(i) Sign in to download full-...