What happens to the value of the expression \dfrac5x+5
x
5
+5start fraction, 5, divided by, x, end fraction, plus, 5 as xxx decreases from a large positive number to a small positive number?
To understand what happens to the value of the expression \(\frac{5}{x} + 5\) as \(x\) decreases from a large positive number to a small positive number, we will analyze the behavior of the two terms separately.
1. Term \(\frac{5}{x}\):
As \(x\) decreases from a large positive number to a small positive number, the denominator \(x\) approaches zero. When dividing a number by a very small positive number (or approaching zero), the result becomes a very large positive number. So, as \(x\) approaches zero from the positive side, the value of \(\frac{5}{x}\) goes to positive infinity.
2. Term 5:
The value of 5 remains constant, regardless of the value of \(x\), as it is independent of \(x\).
Now, when we add the two terms together, we are essentially adding a very large positive number (result of \(\frac{5}{x}\)) and a constant number (5). The sum of a very large positive number and a constant is still a very large positive number.
Therefore, as \(x\) decreases from a large positive number to a small positive number, the value of the expression \(\frac{5}{x} + 5\) increases to positive infinity.