# Find the limit $$\\lim\_{{x \\to \\infty}} \\frac{3x^{-1} - 3x^{-3}}{4x^{-2} + x^{-5}},$$ we need to determine the behavior of the function as ( x ) approaches infinity

**URL:** <https://sorumatik.co/t/find-the-limit-lim-x-to-infty-frac-3x-1-3x-3-4x-2-x-5-we-need-to-determine-the-behavior-of-the-function-as-x-approaches-infinity/83430>\
**Category:** Üniversite Matematik\
**Tags:** ayt-matematik, matematik\
**Created:** [Temmuz 18, 2024, 6:04ös UTC](https://sorumatik.co/t/find-the-limit-lim-x-to-infty-frac-3x-1-3x-3-4x-2-x-5-we-need-to-determine-the-behavior-of-the-function-as-x-approaches-infinity/83430 "2024-07-18T18:04:03Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Muhammed\_Burak\_TÜRKY](https://sorumatik.co/user_avatar/sorumatik.co/muhammed_burak_t%C3%BCrky/32/10409_2.png) [@Muhammed\_Burak\_TÜRKY](https://sorumatik.co/u/Muhammed_Burak_T%C3%9CRKY)\
**Post date:** [Temmuz 18, 2024, 6:04ös UTC](https://sorumatik.co/t/find-the-limit-lim-x-to-infty-frac-3x-1-3x-3-4x-2-x-5-we-need-to-determine-the-behavior-of-the-function-as-x-approaches-infinity/83430/1 "2024-07-18T18:04:03Z")

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![Ekran görüntüsü 2024-07-18 210327](https://sorumatik.co/uploads/default/original/3X/8/2/82287691e075c87c7319e8ba5a01828362bdbbfb.png)

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**Author:** ![Sorumatik\_Ogretmen](https://sorumatik.co/user_avatar/sorumatik.co/sorumatik_ogretmen/32/30517_2.png) [@Sorumatik\_Ogretmen](https://sorumatik.co/u/Sorumatik_Ogretmen)\
**Post date:** [Temmuz 18, 2024, 6:04ös UTC](https://sorumatik.co/t/find-the-limit-lim-x-to-infty-frac-3x-1-3x-3-4x-2-x-5-we-need-to-determine-the-behavior-of-the-function-as-x-approaches-infinity/83430/2 "2024-07-18T18:04:17Z")

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## **Muhammed\_Burak\_TÜRKY said**

 ![Ekran görüntüsü 2024-07-18 210327](https://sorumatik.co/uploads/default/original/3X/8/2/82287691e075c87c7319e8ba5a01828362bdbbfb.png)

**Answer:**  
To find the limit

\lim\_{{x \to \infty}} \frac{3x^{-1} - 3x^{-3}}{4x^{-2} + x^{-5}},

we need to determine the behavior of the function as x approaches infinity.

1. **Rewrite the expression:**

2. **Factor out the dominant term in both the numerator and denominator:**

3. **Simplify the expression by canceling out common terms:**

Therefore, the limit is:

\boxed{\frac{3}{4}}