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1469Repeating-Block Power Series 4Let a n repeat the block [1, 2, 0, 1] forever. Evaluate sum (n=1) inf a n * (1/2) n.数学困难derivation未尝试免费1470Repeating-Block Power Series 5Let a n repeat the block [4, -2, 1] forever. Evaluate sum (n=1) inf a n * (1/6) n.数学困难derivation未尝试面试订阅1476Clipped Floor Integral 1Evaluate integral 0 1 max(x, 1/5) dx.数学简单derivation未尝试免费1498Exponential Tail Integral 3Evaluate integral 0 inf x e (-3x) dx.数学中等derivation未尝试免费1499Exponential Tail Integral 4Evaluate integral 0 inf x 2 e (-2x) dx.数学中等derivation未尝试免费1501Quote Impact Multiplier 1Use a second-order Taylor approximation around 0 to estimate exp(2x)/(1+1x) at x=1/20.数学简单数值题未尝试免费1503Inventory Skew Multiplier 3Use a second-order Taylor approximation around 0 to estimate exp(1x)/(1+-1x) at x=1/25.数学中等derivation未尝试免费1504Spread Fade Multiplier 4Use a second-order Taylor approximation around 0 to estimate exp(-2x)/(1+1x) at x=1/40.数学中等数值题未尝试免费1506Volatility Rescaling Neutralizer 1Choose b so that sqrt(1+6x) * exp(bx) has no linear term in its Taylor expansion around 0.数学简单数值题未尝试免费1511Local Log-Carry Curvature 1Compute the x 2 coefficient in ln(1+5x) - ln(1+2x) - (3)x.数学简单数值题未尝试免费1512Cross-Asset Log Ratio Curvature 2Compute the x 2 coefficient in ln(1+4x) - ln(1+-1x) - (5)x.数学简单数值题未尝试免费1516Levered Book Approximation 1Use a second-order Taylor approximation around 0 to estimate (1+2x) (3/2) * (1+-1x) (-1) at x=1/20.数学简单数值题未尝试免费1517Convex Funding Approximation 2Use a second-order Taylor approximation around 0 to estimate (1+1x) (1/2) * (1+3x) (-1) at x=1/50.数学中等数值题未尝试免费1518Skewed Ratio Approximation 3Use a second-order Taylor approximation around 0 to estimate (1+4x) (-1) * (1+-2x) (1/2) at x=1/25.数学中等derivation未尝试免费1519Adjusted Gross Multiplier 4Use a second-order Taylor approximation around 0 to estimate (1+3x) (2) * (1+1x) (-1) at x=1/40.数学困难derivation未尝试面试订阅1520Local Hedge Multiplier 5Use a second-order Taylor approximation around 0 to estimate (1+-2x) (1/2) * (1+5x) (1/2) at x=1/100.数学困难derivation未尝试面试订阅1521Quadratic Stress Calibration 1Choose c so that exp(2x + c x 2) - 1 - 2x has quadratic coefficient 5.数学简单数值题未尝试免费1523Asymmetric Buffer Calibration 3Choose c so that exp(-1x + c x 2) - 1 - -1x has quadratic coefficient 4.数学中等数值题未尝试免费1526Determinant After a Rank-One Overlay 1An invertible matrix A has det(A) = 12. For vectors u and v, suppose v T A (-1) u = 1/2. What is det(A + u v T)?数学简单数值题未尝试免费1527Stress-Adjusted Determinant 2An invertible matrix A has det(A) = 5. For vectors u and v, suppose v T A (-1) u = -3/5. What is det(A + u v T)?数学简单数值题未尝试免费