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

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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.
  • #1
Arixal
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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.
 
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  • #2
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##.
 
  • #3
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 [itex]\,h\to 0\,[/itex] 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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