Find the limit.
lim (x+2)/(radical(9x^2+1))
x-->infinity
As x-> infinity you can ignore the constant terms in the numerator and denominator, becasue they become negligible in comparison to the term that contains x.
lim x/sqrt(9x^2)= lim x/(3x) = 1/3
thank you, it makes much more sense now
To find the limit as x approaches infinity, we need to determine the behavior of the function as x becomes larger and larger.
Let's simplify the expression first:
lim(x --> infinity) of (x + 2) / sqrt(9x^2 + 1)
Dividing both the numerator and denominator by x, we get:
lim(x --> infinity) of (1 + 2/x) / sqrt((9x^2 + 1) / x^2)
Now, as x approaches infinity, the term 2/x approaches 0, and (9x^2 + 1) / x^2 simplifies to 9. Therefore, the expression becomes:
lim(x --> infinity) of (1 + 0) / sqrt(9)
This further simplifies to:
lim(x --> infinity) of 1 / 3
Thus, the limit as x approaches infinity of (x + 2) / sqrt(9x^2 + 1) is 1/3.