# Limit of Lim h->0 ((2+h^2) - 8)/h

• Arixal
In summary, the conversation discusses a limit problem involving an expression with h approaching 0. The limit was defined, but the details were forgotten. The poster is seeking an explanation from others. One user provides a possible solution involving a correction to the initial expression.
Arixal
I saw my professor solve for the limit of ((2+h)2 - 8)/h as h approaches 0 and it was defined, but for the life of me I can't remember how. Everyone I have asked can't seem to figure it out either, so I was hoping someone here could explain.

Arixal said:
I saw my professor solve for the limit of ((2+h)2 - 8)/h as h approaches 0

I'm going to assume the thread title is a typo.

and it was defined

Hint: let ##h = 0.1, 0.01, 0.001, \ldots## and manually calculate the expression for each ##h##.

Arixal said:
I saw my professor solve for the limit of ((2+h)2 - 8)/h as h approaches 0 and it was defined, but for the life of me I can't remember how. Everyone I have asked can't seem to figure it out either, so I was hoping someone here could explain.

You wrote

$$\frac{(2+h)^2-8}{h}$$

and the limit of this thing when $\,h\to 0\,$ doesn't exist. But perhaps you meant

$$\lim_{h\to 0}\frac{(2+h)^3-8}{h}=\lim_{h\to 0}\frac{8+12h+6h^2+h^3-8}{h}=\lim_{h\to 0}\;(12+6h+h^2)=12$$

DonAntonio

## 1. What is the limit of the expression Lim h->0 ((2+h^2) - 8)/h?

The limit of the expression Lim h->0 ((2+h^2) - 8)/h is undefined.

## 2. What is the significance of the "h" in the expression Lim h->0 ((2+h^2) - 8)/h?

The "h" in the expression represents the change in the input value, which approaches 0 in this limit. It is used to evaluate the behavior of the function as the input approaches a specific value.

## 3. Can the limit of the expression Lim h->0 ((2+h^2) - 8)/h be solved algebraically?

No, the limit cannot be solved algebraically. It requires the use of calculus techniques such as L'Hospital's rule or the limit definition of derivative.

## 4. How does the graph of the function represented by the expression Lim h->0 ((2+h^2) - 8)/h look like?

The graph of the function is a vertical line, as the limit approaches infinity from both sides. It has a vertical asymptote at x=0.

## 5. What are some real-life applications of evaluating the limit of the expression Lim h->0 ((2+h^2) - 8)/h?

The limit can be used to calculate instantaneous rates of change in physics and engineering problems, such as finding the velocity of an object at a specific point in time. It is also used in economics and finance to model and predict changes in variables over time.

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