Find limit as x goes to infinity of (6x-(1/4x))/(3x-(1/x))?
one half
–4
negative one fourth
2
To find the limit as x goes to infinity of the given expression, we need to determine the behavior of the numerator and the denominator as x approaches infinity.
Let's start by analyzing the numerator: 6x - (1/4x)
As x approaches infinity, the (1/4x) term becomes smaller and smaller since x is getting larger and larger. Thus, we can neglect the (1/4x) term when considering the limit. Therefore, the numerator simplifies to 6x.
Next, let's analyze the denominator: 3x - (1/x)
As x approaches infinity, the (1/x) term becomes smaller and smaller, and we can once again neglect it when considering the limit. Therefore, the denominator simplifies to 3x.
Now we can rewrite the expression with the simplified numerator and denominator:
Limit as x approaches infinity of (6x)/(3x)
Now we can cancel out the common factors of x in the numerator and denominator:
Limit as x approaches infinity of 6/3
Simplifying further, we have:
Limit as x approaches infinity of 2
Therefore, the limit as x approaches infinity of the given expression is 2.