lim-(x?8)??(x+vx)/(3x+2vx+1)?

Question

lim-(x→∞)??(x+√x)/(3x+2√x+1)?

Answer 1

Lim_x→∞[(x+√x)/(3x+2√x+1)] 

 

This limit has the indeterminate form ∞/∞.

 

Divide the numerator and denominator by x (the highest power of x that appears in the denominator) and simplify:

 

We get:  lim_x→∞[(1 + 1/√x)/(3 + 2/√x + 1/x)]

 

                   As x→∞, 1/√x, 2/√x, and 1/x all approach 0

 

So the limit above = (1+0)/(3+0+0) = 1/3