Is this the correct answer? Thanks...

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In summary, the limit of (2x^2-x-3)/(x+1) as x approaches -1 is equal to 1. You can simplify the expression and evaluate by substitution or use L'Hospital's rule. Both methods result in the same answer of -5.
  • #1
ladyrae
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Thanks...

Evaluate the limit

lim x->-1 (2x^2-x-3)/(x+1)

I simplified to (2x^2-3)/(2x+1) = -1/-1 = 1

Is this correct?
 
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  • #2
I believe you want to factor the top, cancel out the hole in the graph, and then evaluate by substitution.

[tex]\lim_{x\rightarrow -1} \frac {2x^2-x-3}{x+1}[/tex]

[tex]= \lim_{x\rightarrow -1} \frac {(2x-3)(x+1)}{x+1}[/tex]

[tex]= \lim_{x\rightarrow -1} 2x-3[/tex]

= -5.
 
  • #3
You can use L'Hospital's rule:

[tex]\lim_{x\rightarrow -1} \frac {2x^2-x-3}{x+1}[/tex]

If you plug in, you get 0/0, so:

[tex]\lim_{x\rightarrow -1} \frac {2x^2-x-3}{x+1}[/tex]
= [tex]\lim_{x\rightarrow -1} \frac {4x-1}{1}[/tex]

Plug in and you get -5.
 

1. What does the term "limit" refer to in mathematics?

The term "limit" refers to the value that a function or sequence approaches as its input or index approaches a specific value. It is used to describe the behavior of a function or sequence as it gets closer and closer to a particular point.

2. How is a limit evaluated?

A limit is evaluated by substituting the value the function or sequence is approaching into the expression and simplifying it. If the resulting value is undefined, then other methods such as L'Hopital's rule or graphing may be used to evaluate the limit.

3. What does it mean if a limit does not exist?

If a limit does not exist, it means that the function or sequence does not approach a specific value as its input or index approaches a certain value. This could be due to a discontinuity in the function or an oscillating behavior.

4. Can a limit be infinite?

Yes, a limit can be infinite. This means that the function or sequence approaches positive or negative infinity as its input or index approaches a specific value. This can happen when the function has a vertical asymptote or when the sequence grows without bound.

5. Why are limits important in mathematics?

Limits are important in mathematics because they allow us to describe and analyze the behavior of functions and sequences as they approach a specific value. They are also essential in the development of calculus and in solving problems in physics, engineering, and other fields.

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