# Confusion about the Heaviside method

#### ali PMPAINT

Problem Statement
described on picture
Relevant Equations
described on picture
So, Heavside's method confused me, I mean, but we can't divide by zero, can we?

So, my mind sees it as cheating, and to multiply both sides by zero to cancel zeros, and for the example above(from Thomas Calulus), when x = 1, before you multiply by x-1(=0), you get: 2/0=A/0+B/-1+c/-2, and I think you get the point where I am confused, where am I misunderstanding Heavside's method?

Related Precalculus Mathematics Homework News on Phys.org

#### Phylosopher

But it is not multiplied by zero. It is multiplied by the variable $x-1$.
Either case, before or after canceling $x-1$. The equality holds for the limit $x=1$.

You cannot cancel zeros, but you can cancel expressions, because same expressions have the same behavior (Same value at any chosen point). Take the following:

$$\lim_{x\rightarrow 0} \frac{x}{x}=1$$

Even without cancelling the terms $x$, the limit is $1$. Although, approaching the function $x$ itself is zero. Cancelling expressions is not the same as cancelling numbers.

You can check the previous with a simple table, approaching zero from the left and the right of $x$.

**Not an expert, but this is what I think.

#### ali PMPAINT

You cannot cancel zeros, but you can cancel expressions, because same expressions have the same behavior (Same value at any chosen point). Take the following:

$$\lim_{x\rightarrow 0} \frac{x}{x}=1$$
Well, you're kind of right, but $$\lim_{x\rightarrow 0} \frac{x}{x}=1$$ doesn't imply x/x = 1 when x = 0, does it?
So, if you're saying that we should take the limit as x is approaching to a specific number, like 1 on the first post example, it doesn't mean that the value EQUALS the number it approaches, so, although I liked your reasoning, I'm still not convinced.

#### Phylosopher

\lim_{x\rightarrow 0} \frac{x}{x}=1 doesn't imply x/x = 1 when x = 0, does it?
The limit is 1 for $x\rightarrow 0$.

Well, it is more like a removable discontinuity. Sadly, this is my best explanation, maybe others can help us understand.

### Want to reply to this thread?

"Confusion about the Heaviside method"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving