Define (a) P.T. f(x) 0. (b) P.T. f(x) = x+1 [*** sin(1²) dt x 2x f(x) = cos(x²) - cos[(x + 1)²] +r(x)

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Q: Give all the possible elementary divisors of a group of order 40.

A: 40=23×5 So, the possible elementary divisors of the group are 2,2,2,5,2,4,5 and 8,5

Q: (a) f(x) = sin(x) X at x = 0.

A: a.the function is not defined at x=0. The function has right hand and left-hand limits same and…

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A: a= 8.   See the attachment for the complete solution.

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A: Leibnitz Rule of differentiation:       ddx ∫α(x)β(x) f(x,t) dt =∫α(x)β(x) d(f(x,t))dx dt +d(β(x))dx…

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A: We have to solve given problem:

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A: The answer of above solution is option A. i.e true.

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A:

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A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

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A: Topic = Derivative

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A: Using substitution then integrating we get correct answer as (C)

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A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer three subparts…

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A:

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A: We have to prove ∫x-32J52(x)dx=2πcosxx2-sinxx3+C