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1446Mixed-Expansion Limit 1Compute lim (x->0) [((e x - 1) - ln(1+x)) / x 2].数学简单数值题未尝试免费1447Mixed-Expansion Limit 2Compute lim (x->0) [((sqrt(1+x) - sqrt(1-x)) - x) / x 3].数学简单数值题未尝试免费1448Mixed-Expansion Limit 3Compute lim (x->0) [ln(1+2x) - 2 arctan(x)] / x 2.数学中等数值题未尝试免费1449Mixed-Expansion Limit 4Compute lim (x->0) [e x cos(x) - 1 - x] / x 2.数学中等数值题未尝试免费1450Mixed-Expansion Limit 5Compute lim (x->0) [ln(cosh(2x))] / x 2.数学困难数值题未尝试面试订阅1451Alternating-Input Recurrence 1A sequence satisfies x (n+1) = 1/2 x n + c n, where c n = 1 on odd n and c n = 3 on even n. Assuming any starting value x 1, what are the limits of the even and odd subsequences?数学简单数值题未尝试免费1456Contracting Second-Order Limit 1A sequence obeys x (n+2) = 1/4 x (n+1) + 1/5 x n + 3. If the sequence converges, what must its limit be?数学简单数值题未尝试免费1462Spaced-Pole Telescoping Series 2Evaluate the infinite series sum (n=1) inf 1 / [(4n+1)(4n+1+4)].数学简单derivation未尝试免费1466Repeating-Block Power Series 1Let a n repeat the block [1, 0, 2] forever. Evaluate sum (n=1) inf a n * (1/3) n.数学简单数值题未尝试免费1467Repeating-Block Power Series 2Let a n repeat the block [2, -1] forever. Evaluate sum (n=1) inf a n * (1/4) n.数学中等derivation未尝试免费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