Question

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x → 0 x 8x 8x − 1

Answer 1

1/log8

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