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Question

Evaluate :
limxx2(x+2x3x+3x)

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Solution

We have,
limxx2(x+2x3x+3x)limxx2⎜ ⎜(1+2x)12(1+3x)13⎟ ⎟limxx2⎢ ⎢ ⎢ ⎢⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪1+1.22x+12(121)2.(2x)2+.........⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪1+1.33x+13(131)2.(3x)2+.........⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎥ ⎥ ⎥ ⎥limxx2x2[18×4+19×9+........]=12+1=12

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