10. Let w = f(x, y, z) = xe. If x = t², y = 1-t₁ z = 1 + 2t, use the partial dw dt derivatives and the chain rule to find

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A: We can answer the question as below.

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A: This question can be solved using the concept of geometry to solve definite integrals.

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A: Please see the below picture for detailed solution.

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A: See this solution in below

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A: Please see the below picture for detailed solution.

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A: According to Bartleby guidelines I can only answer the first three sub questions of the given…

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A: We have to find the limit using L Hospital rule.

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A: To find 2AB +3 AC

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A: Please see the answer below.

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A: To  find the  limit.

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A: To solve the given integral problem by substitution.

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A: We can solve the given initial valued problem .

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A: Authoring guidelines: As per the authoring guidelines, we can solve only the first three parts of…

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A: We need to evaluate integral.

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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