Question

What is the limit as x approaches infinity of (3x - 5) / (2x + 7)?

Answer 1

To find the limit as x approaches infinity of (3x - 5) / (2x + 7), we need to examine the behavior of the expression as x gets larger and larger.

When x approaches infinity, the highest power of x in the numerator and denominator will dominate the expression. In this case, the highest power of x is x in both the numerator and denominator.

Therefore, we can simplify the expression by dividing both the numerator and denominator by x:

(3x - 5) / (2x + 7) = (3 - 5/x) / (2 + 7/x)

As x gets larger and larger, the value of 5/x approaches zero, and the value of 7/x approaches zero. Therefore, we can simplify the expression further:

(3 - 0) / (2 + 0) = 3/2

Therefore, the limit as x approaches infinity of (3x - 5) / (2x + 7) is 3/2.

Answer 2

The limit as x approaches infinity of (3x - 5) / (2x + 7) is:

3/2

To see this, we can divide both the numerator and denominator by the highest power of x:

(3x - 5) / (2x + 7) = (3 - 5/x) / (2 + 7/x)

As x approaches infinity, the fraction 5/x and 7/x become negligible, hence:

lim [(3 - 5/x) / (2 + 7/x)] = 3/2