Indeterminant forms homework help

In summary, the problem involves finding the limit of a function as x approaches infinity. The attempt at a solution involved using L'Hospital's Rule, but this led to ∞-∞ in the numerator or denominator. The suggestion was made to use the conjugate trick and simplify the expression, ultimately arriving at the answer of 2.5. The student thanks their peers for their help in solving the problem.
  • #1
EngnrMatt
34
0

Homework Statement



lim{x[itex]\rightarrow∞[/itex]} sqrt(x^(2)+5x+11)-x

Homework Equations



I know it is of type ∞-∞

The Attempt at a Solution



I have worked this problem around to death, and I know I'm supposed to give them a common denominator to get ∞/∞ and use L'Hospital's Rule, but I end up with ∞-∞ in the numerator or the denominator every time. Professor never went over problems this complex in class, and now we are too far ahead of this section to ask her to waste time going back to it.

I know the answer is 2.5 (graphing calculator), but my problem is figuring out how to work it.
 
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  • #2
Try multiplying and dividing by sqrt(x^(2)+5x+11)+x. It's the 'conjugate' trick. It will turn out you don't really even need l'Hopital. You can do it all with algebra.
 
  • #3
You are right you can use i'Hopital but after one differentiation, use: $$\sqrt{x^2 + 5x + 11} = \sqrt{x^2} \sqrt{1 + 5/x + 11/x^2}, $$ simplify and cancel terms and then take x → ##\infty##.
 
  • #4
Thanks guys! I knew it had something to do with the conjugate, but for some reason I had trouble remembering just how it worked. I've worked it out now though, thanks for the help!
 

Related to Indeterminant forms homework help

1. What are indeterminate forms in calculus?

Indeterminate forms in calculus refer to mathematical expressions that cannot be easily evaluated using traditional methods. These forms arise when there is a lack of information or when two or more limiting values are competing with each other.

2. How do I solve indeterminate forms?

There are several techniques for solving indeterminate forms, including L'Hospital's Rule, factoring and cancelling, and substitution. The specific method used will depend on the type of indeterminate form and the context of the problem.

3. Can indeterminate forms have multiple solutions?

Yes, indeterminate forms can have multiple solutions. This is because these forms arise when there is a conflict between two or more limiting values. The solution obtained will depend on the method used to evaluate the form.

4. Why are indeterminate forms important?

Indeterminate forms are important because they often arise in real-world problems and are used to model various phenomena. They also help us understand the concept of infinity and the behavior of functions near their asymptotes.

5. Where can I find help with indeterminate forms homework?

You can find help with indeterminate forms homework from various online resources, such as math forums, tutoring websites, and educational videos. Your teacher or professor may also be able to provide additional assistance and clarification.

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