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A: Please find attachment for the details solution

Q: Please answer with explanation. I will really upvote

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Q: #1. ii. Thanks

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A: Solve the equations

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A: Since you have posted a multi subparts question according to guildlines I will solve first three que...

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A: We have to check the given function is continuous at x=0.

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A: We have to prove by induction.

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A: According to our guidelines ,  i will solve only first three subparts. 

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A: We have to find the solution of differential equation.

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A:   Since you have posted a multi subparts question according to guildlines I will solve first three q...

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A: Please find the detailed solution in next step