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

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

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

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)