31. (a) Use the Quotient Rule to differentiate the function tan x f(x) see x (b) Simplify the expression for /(x) by writing it in terms of sin x and cos x, and then find /(x). (c) Show that your answers to parts (a) and (b) are equivalent.

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A: We will find the limits. 

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A: For the following problem,

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A: Given

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A: Topic:-  limits   

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A: We can find the required acceleration as below.

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A: Let's find. 

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A:

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A: The solution is given in the next step.

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A: Topic:- simplification

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A: This question is based on indefinite integral.

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A:

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A:

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A: topic - condition for differentiable function

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A:

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A: The objective is to critique the validity of the expression. 

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A: Since you have posted multiple question in this question which are not interlinked so i have solved ...

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A: Given problem:-  

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A: topic- functions

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A:

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A: We have to solve the aseries as per question. 

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A: Given :0.101010...

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A: follow next step

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A:

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A: Let's find.