Answer:
1/log8
Step-by-step explanation:
Given the limit of the function
Lim x → 0 x•8^x/8^x − 1
Plug in the value of x
= 0•8^0/8^0-1
= 0(1)/1-1
= 0/0 (indeterminate)
Apply l'hosipitals rule:
Lim x → 0 d/dx(x•8^x)/d/dx(8^x − 1)
= Lim x → 0 (x•8^xlog8+1(8^x))/8^xlog8
Plug in the value of x:
= 0•8^0log8+8^0/8^0log8
= 0•1(log8)+1/1•log8
= 0(log8)+1/log8
= 0+1/log8
= 1/log8
Hence the limit of the function is 1/log8
