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4953Boundary Eigenvalue 3For y'' + λ y = 0 on [0,1] with y'(0)=0 and y(1)=0, what is the 1-th positive eigenvalue?数学中等数值题未尝试面试订阅4954Boundary Eigenvalue 4For y'' + λ y = 0 on [0,1.5] with y(0)=0 and y(1.5)=0, what is the 2-th positive eigenvalue?数学中等数值题未尝试面试订阅4956Infer Poisson Forcing From Arc Maximum 13Let y solve y'' = -c on [0,1] with y(0)=0 and y(1)=0. If the maximum value of y on the interval is 0.25, what c is implied?数学中等数值题未尝试面试订阅4957Infer Poisson Forcing From Arc Maximum 14Let y solve y'' = -c on [0,2] with y(0)=0 and y(2)=0. If max y = 2.5, what c is implied?数学中等数值题未尝试面试订阅4958Infer Poisson Forcing From Arc Maximum 15Let y solve y'' = -c on [0,3] with y(0)=0 and y(3)=0. If the maximum value is 1.6875, what c is implied?数学中等数值题未尝试面试订阅4959Infer Poisson Forcing From Arc Maximum 16Let y solve y'' = -c on [0,1.5] with y(0)=0 and y(1.5)=0. If max y = 1.125, what c is implied?数学中等数值题未尝试面试订阅4961Shooting Method Diagnostic 18Why does the shooting method for a second-order BVP usually search over one missing initial slope rather than over an entire function?数学困难essay未尝试面试订阅4962Multiplicity Diagnostic 19Why can a boundary value problem have multiple solutions even when the corresponding initial-value problem is unique for each chosen slope?数学困难essay未尝试面试订阅4963Neumann Compatibility Diagnostic 20Why does a pure Neumann problem for y'' = f sometimes need a compatibility condition before any solution can exist?数学困难essay未尝试面试订阅4964Finite-Difference Diagnostic 21Why can a finite-difference solve be more numerically stable than naive shooting for a stiff BVP?数学困难essay未尝试面试订阅5850Alternating Geometric SumEvaluate the infinite series sum (n=0) inf 5 * (-2/3) n.数学简单数值题未尝试免费5851Telescoping Log Partial SumFind the value of the partial sum S N = sum (n=1) N ln(1 + 1/n), and state whether the full series converges.数学简单数值题未尝试免费5852Nested Radical Fixed PointA sequence is defined by x 1 = 1 and x (n+1) = sqrt(2 + x n). Assuming it converges, find its limit.数学中等数值题未尝试免费5853Radius of Convergence via Ratio TestDetermine the radius of convergence of the power series sum (n=1) inf (3 n / n) x n.数学中等数值题未尝试免费5854Reciprocal Product SeriesEvaluate the infinite series sum (n=1) inf 1 / (n(n+1)).数学简单数值题未尝试免费5855p-Series Convergence ThresholdFor which of the following exponents p does the series sum (n=1) inf 1/n p converge: p = 1/2, p = 1, p = 3/2, p = 2? List all values for which it converges.数学简单数值题未尝试免费5856Compound-Limit ExponentialEvaluate the limit of the sequence a n = (1 + 3/n) n as n -> inf. Give the exact value and a decimal to three places.数学中等数值题未尝试免费5857Arithmetico-Geometric SeriesEvaluate the infinite series sum (n=1) inf n * (1/2) n.数学中等数值题未尝试免费5858Integrating Factor with Variable CoefficientSolve the first-order linear ODE x'(t)+\dfrac x(t) t =t for t>0 with x(1)=2, and evaluate x(2).数学中等derivation未尝试面试订阅5859Separable Nonlinear ODE and Blow-UpSolve the separable ODE y'(x)=x\,y(x) 2 with y(0)=1. At what value of x>0 does the solution blow up?数学中等derivation未尝试面试订阅