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

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

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!