Question

find the limit. write ∞ or - ∞ where appropriate.
lim(x→0⁺) - 1/(5x)
lim(x→0⁺) - 1/(5x)=□ (simplify your answer.)

Explanation:

Step1: Analyze the behavior as x approaches 0 from the right

As \(x\to0^{+}\), \(x\) is a small positive number. So \(5x\) is also a small positive number.

Step2: Consider the fraction \(-\frac{1}{5x}\)

Since \(5x>0\) as \(x\to0^{+}\), then \(-\frac{1}{5x}<0\). And as \(x\) gets closer and closer to \(0\) from the right, the value of \(\frac{1}{5x}\) gets larger and larger in the positive - direction, so \(-\frac{1}{5x}\) gets larger and larger in the negative - direction.

Answer:

\(-\infty\)