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If x 1 (5x+1)1/3-(x+5)1/3(2x+3)1/2-(x+4)1/2= m 5n(2n)2/3, where (m, n)=1, then 8m+12n is equal to .
100
00 form L'Hôpital's rule (differentiate Nr and Dr, put x=1):
Nr' = 53(6)-2/3- 13(6)-2/3= 43 6-2/3
Dr' = 22(5)-1/2- 12(5)-1/2= 12 5
Limit = 43 2 562/3= 8 53(2 3)2/3
m=8, n=3
8m+12n=64+36=100
Answer: 100
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