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Taylor Series in 2 Variables- HW Problems
Find the second order Taylor formula around (0,0) and approximate
the value of 𝑓(0.1, 0.5).
1. 𝑓(𝑥, 𝑦) = 𝑒 𝑦 sin(𝑥 )
2 −𝑦 2)
2. 𝑓(𝑥, 𝑦) = 𝑒 (−𝑥 sin(𝑥𝑦)
3. Let 𝑓 (𝑥, 𝑦) = 𝑥𝑠𝑖𝑛(𝑦) − 𝑦𝑐𝑜𝑠(𝑥 ). Find the second order Taylor
𝜋
polynomial at the point (𝜋, 2 ). Use this formula to approximate
𝜋
𝑓(𝜋 + 0.1, − 0.1).
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Taylor Series in 2 Variables- HW Problems
Find the second order Taylor formula around (0,0) and approximate
the value of 𝑓(0.1, 0.5).
1. 𝑓(𝑥, 𝑦) = 𝑒 𝑦 sin(𝑥 )
2 −𝑦 2)
2. 𝑓(𝑥, 𝑦) = 𝑒 (−𝑥 sin(𝑥𝑦)
3. Let 𝑓 (𝑥, 𝑦) = 𝑥𝑠𝑖𝑛(𝑦) − 𝑦𝑐𝑜𝑠(𝑥 ). Find the second order Taylor
𝜋
polynomial at the point (𝜋, 2 ). Use this formula to approximate
𝜋
𝑓(𝜋 + 0.1, − 0.1).
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