Lim x→inf text book example confusing step

In summary, "Lim x→inf" is a mathematical notation used to represent the limit of a function as the variable x approaches infinity. The "textbook example confusing step" is a common problem that students encounter when learning about limits and can be overcome by breaking down the problem and seeking clarification. Tips for understanding the confusing step include carefully reviewing algebraic steps and using visual aids, and this understanding can also be applied to real-world problems to ensure accurate results.
  • #1
cambo86
25
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I was hoping someone could clarify a step of an example in my calculus textbook.

lim x→∞ (√(2*x2+1))/(3*x-5) = lim x→∞ (√(2+(1/x2)))/(3-(5/x)), (since √x2=x for x>0)

The description for the step says to divide numerator and denominator by x.

I understand to divide top and bottom of a rational function by the xn where n is the highest power of x that occurs in the denominator in this situation but I don't understand how the numerators equate in this equation.
 
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  • #2
For x > 0, (1/x) sqrt( 2x^2 + 1) = sqrt(1/x^2) sqrt(2x^2 + 1) = sqrt( (1/x^2)(2x^2 + 1) )
 

1. What does "Lim x→inf" mean in the context of a textbook example?

"Lim x→inf" is a mathematical notation used to represent the limit of a function as the variable x approaches infinity. It indicates that we are interested in the behavior of the function as the input values get larger and larger.

2. Why is the "textbook example confusing step" often mentioned in discussions about limits?

The "textbook example confusing step" refers to a common problem that many students encounter when learning about limits. It usually involves a step in the calculation that is not clearly explained or justified, causing confusion for the reader.

3. How can I overcome confusion about the "textbook example confusing step" when studying limits?

One way to overcome confusion about the "textbook example confusing step" is to break down the problem into smaller, simpler steps. This can help to identify where the confusion arises and allow for a better understanding of the concept. Additionally, seeking clarification from a teacher or tutor can also be helpful.

4. Are there any tips for understanding the "textbook example confusing step" in limit calculations?

One tip for understanding the "textbook example confusing step" is to carefully review the algebraic steps used in the calculation. Pay attention to any assumptions or manipulations made, and make sure they are justified and in line with the rules of limit calculations. Drawing graphs or using numerical examples can also aid in understanding the concept.

5. How can I apply my understanding of the "textbook example confusing step" to real-world problems?

In real-world applications, the "textbook example confusing step" can represent a potential source of error or misinterpretation. By developing a strong understanding of the concept, you can better identify and address any potential issues in your calculations, allowing for more accurate and reliable results.

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