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Question

limxx5tan(1πx2)+3|x|2+7|x|3+7|x|+8is equal to


A

1/π

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B

0

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C

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D

Does not exist

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Solution

The correct option is A

1/π


limxx5tan(1πx2)+3|x|2+7|x|3+7|x|+8limxx5tan(1πx2)+3x2+7x37x+8 [ x<0|x|=x]On dividing the numerator and denominator by x3limxx2tan(1πx2)+3x+7x317x2+8x3limx1πtan{1πx2}+3x+7x31(πx2)17x2+8x3

Since [x1πx20 and limθ0tanθθ=1]=1π.1+0+010+0=1π


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