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1436Cosine Defect at Double FrequencyCompute lim x->0 [1 - cos(2x)] / x 2.数学简单数值题未尝试免费1437Cube-Root LinearizationCompute lim x->0 [ (1+2x) (1/3) - 1 ] / x.数学简单数值题未尝试免费1438Sequence Limit From a Square RootCompute lim n->∞ n[(1+2/n) (1/2) - 1].数学中等数值题未尝试免费1439Logarithmic Sequence CorrectionCompute lim n->∞ n 2 [ln(1+1/n) - 1/n].数学困难数值题未尝试面试订阅1440Square-Root Remainder 5Compute lim (x->0) [sqrt(1 + 3x + -4x 2) - 1 - (3/2)x] / x 2.数学困难数值题未尝试面试订阅1441Trigonometric Asymptotic 1Compute lim (x->0) [sin(2x + 7x 2) - 2x] / x 2.数学简单数值题未尝试免费1442Exponential Minus CosineCompute lim x->0 [e x - cos x - x] / x 2.数学中等数值题未尝试免费1443Arcsine Cubic RemainderCompute lim x->0 [arcsin x - x] / x 3.数学中等数值题未尝试免费1444Trigonometric Asymptotic 4Compute lim (x->0) [arctan(5x) - 5x] / x 3.数学困难数值题未尝试面试订阅1445Product-Log CancellationCompute lim x->0 [ (1+x)ln(1+x) - x ] / x 2.数学困难数值题未尝试面试订阅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