Limit of [(7x^2)-x+11]/(4-x) as x->-infinity

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In summary, the conversation revolved around finding the limit of a function as x approaches negative infinity. The initial attempt using L'Hopital's rule resulted in an indeterminate form, and the idea of dividing both the numerator and denominator by x was suggested as an alternative method. It was eventually determined that the answer should be infinity, even without using L'Hopital's rule. The conversation also touched on the confusion and challenges of working with limits involving infinity.
  • #1
kemmy
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Homework Statement



Find the Limit (as x-> -infinity) of [(7x^2)-x+11]/(4-x)

So I found that the limit is infinity/infinity indeterminate form so I tried to use L'hopital's to solve it.
So I took the derivative of (7x^2)-x+11 and got 14x-1
then for the derivative of 4-x I got -1

So the Limit as x->-infinity of 14x-1/-1 would be -infinity/-1 . So would the limit be infinity?

Apparently this answer is wrong. ...Is there a reason L'Hopital's wouldn't work here? How can I solve this?
Any help available would be much appreciated, thanks!
 
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  • #2
The answer should be infinity, even without l'Hospital's, simply by virtue of the quadratic in the numerator. Check to you have the right equation or right way of checking the answer.
 
  • #3
Why use L'Hopital? Divide both numerator and denominator by x. All fractions with x in the denominator will go to 0. What is left?
 
  • #4
Okay... that does make sense. Thanks. I get so confused with Limits working with infinity I just always manage to get myself turned around. Thanks for all the help!
 
  • #5
HallsofIvy said:
Why use L'Hopital? Divide both numerator and denominator by x. All fractions with x in the denominator will go to 0. What is left?

Denominator should be -1 right ? :smile:
unless you plug in infinity after you applied L'Hopital and divide both numerator and denominator by x.
 

1. What is L'Hopital's rule?

L'Hopital's rule is a mathematical technique used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. It states that for a function f(x) and g(x) where both approach 0 or ∞ as x approaches a certain value, the limit of the quotient f(x)/g(x) is equal to the limit of the quotient of their derivatives f'(x)/g'(x).

2. When should L'Hopital's rule be used?

L'Hopital's rule should only be used when the limit of a function results in an indeterminate form, such as 0/0 or ∞/∞. It cannot be applied to limits that result in a definite value or infinity.

3. What is the process of using L'Hopital's rule?

The process of using L'Hopital's rule involves taking the derivative of both the numerator and denominator of the original function, then evaluating the limit again using the new quotient. This process can be repeated multiple times until an answer is obtained or until it is determined that the limit does not exist.

4. Are there any limitations to L'Hopital's rule?

Yes, there are limitations to L'Hopital's rule. It can only be applied to limits of indeterminate forms, not to limits that result in a definite value or infinity. It also cannot be used if the original function does not have a derivative at the point where the limit is being evaluated.

5. Can L'Hopital's rule be used with any type of function?

No, L'Hopital's rule can only be used with functions that are continuous and differentiable in the interval surrounding the point where the limit is being evaluated. It also cannot be used with functions that are not defined for all values of x in the interval.

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