Evaluate the limit. lim x-> infinity n/3^x

0

Step-by-step explanation:

Find the following limit:

lim_ (x->∞) 3^ (-x) n

Applying the quotient rule, write lim_ (x->∞) n 3^ (-x) as (lim_ (x->∞) n) / (lim_ (x->∞) 3^x):

n / (lim_ (x->∞) 3^x)

Using the fact that 3^x is a continuous function of x, write lim_ (x->∞) 3^x as 3^ (lim_ (x->∞) x):

n/3^ (lim_ (x->∞) x)

lim_ (x->∞) x = ∞:

n/3^∞

n/3^∞ = 0:

Answer: 0