Question on lim x→1 (x − 5) / (x^2 + 2x − 4) ?

  • Thread starter alaa amed
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In summary, the question asks whether the statement is true or false and the student is unsure how to solve the left hand side of the equation because the quadratic cannot be factored. The student also mentions that the right hand side of the equation equals 4. The question concludes with asking if the limit of the LHS expression can be evaluated without factoring the quadratic.
  • #1
alaa amed
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Homework Statement



Determine whether the statement is true or false. lim x→1 (x − 5) / (x^2 + 2x − 4) = lim x→1 (x − 5) / lim x→1 (x^2 + 2x − 4)?


Homework Equations


[/B]

The Attempt at a Solution


I know that the right side of this equation and the left side have to equal each other in order for this to be true. On the right hand side the answer is 4. I don't know how to solve the left hand side because (x^2 + 2x − 4) cannot be factored.
 
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  • #2
alaa amed said:

Homework Statement



Determine whether the statement is true or false. lim x→1 (x − 5) / (x^2 + 2x − 4) = lim x→1 (x − 5) / lim x→1 (x^2 + 2x − 4)?


Homework Equations


[/B]

The Attempt at a Solution


I know that the right side of this equation and the left side have to equal each other in order for this to be true. On the right hand side the answer is 4. I don't know how to solve the left hand side because (x^2 + 2x − 4) cannot be factored.
That's irrelevant. Can the limit of the LHS expression be evaluated without factoring the quadratic?
 

1. What is the limit of the function as x approaches 1?

The limit of the function as x approaches 1 is undefined, as the denominator approaches 0 and results in a division by 0 error.

2. How do you determine the limit of a rational function?

To determine the limit of a rational function, factor both the numerator and denominator and simplify the expression. Then, plug in the approaching value for x and evaluate the expression.

3. Can the limit of a rational function be a non-numerical value?

No, the limit of a rational function can only be a numerical value or undefined.

4. Is there a shortcut or trick to solving limits of rational functions?

Yes, if both the numerator and denominator share a common factor, it can be canceled out to simplify the expression and make it easier to evaluate the limit.

5. What is the significance of the limit of a function?

The limit of a function gives us information about the behavior of the function as the input approaches a certain value. It can also help us determine the continuity of a function and identify any points of discontinuity.

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