MTH281 MATHMATICAL METHOD 1 TMA3 QUESTION AND ANSWER

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Question 1. compute the first derivative  F(x) 2x5 + x3/2 - 1/2x

answer is f(x) = 10x4 - 3/2x1/2 + 1/2x2, 40x3 + 3/3x1/2 - 1/x3, - 120x2 - 3/8x - 3/2 + 3/x4

question 2. use leibnitz theorem to evalute the fourth derivative of (2x3 + 3x2 +x +2 )e2x

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answer is 16(2x3 + 15x2 + 31x + 19)e2x

Question 3. find the total differential of function f(x,y) = yex+y

answer is df = [yex+y]dx + [(1+y) ex+y ]dy

Question 4. obtain the n-th differential coefficient of y = (x2+1)ex2

answer is 2n-2e2x (4x2+4nx + n2 - n +4)

Question 5. compute the third derivative of sinxInx using leibnitz theorem

Question 6. find the total differential  of the function f(x,y) = x2 + 3xy with respect to x, given that y = sin-1x

answer is 2x + 3sin-1x + 3x/(1+x2)1/2

 

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