joshiemen said:Homework Statement
Lim x>1 (y^1/3-1)/((y^1/5-1)
Homework Equations
Difference of powers a^n-b^n=(a-b)*(a^n-1*b^0+a^n-2*b^1...+b^n-1)
The Attempt at a Solution
Scanned and attached the solution...
Can anyone Pls explain the steps in the solution, especially, how you factor out such an ugly function.
icystrike said:you can actually substitute y=x^15 , as y>1 , x>1
hence obtaining x>1 (x^5-1)/(x^3-1)
try to divide x-1 from top and bottom
There is this identity:
x^n -1 =(x-1)[x^(n-1) + x^(n-2) + ... + 1 ]
Continue from here =D
Mentallic said:[tex]y-1\equiv (y^{1/3})^3-1\equiv (y^{1/n})^n-1[/tex], n being a natural number.
Does this clear things up?
joshiemen said:Could you elaborate on this further pls? not so clear, i have been staring at it and thinking, have not penetrated the wall of ignorance yet.
A limit problem is a mathematical concept that involves finding the value that a function approaches as its input approaches a specific value. This can help determine the behavior of a function near a particular point.
To solve a limit problem, you can use various techniques such as algebraic manipulation, substitution, and using standard limit rules. It is also helpful to graph the function to gain a visual understanding of its behavior near the limit point.
The most common types of limit problems include limits at a finite point, limits at infinity, and limits involving trigonometric, exponential, or logarithmic functions.
Limit problems are important because they are used to analyze the behavior of functions, which is crucial in various fields such as physics, engineering, and economics. They also help in determining continuity, differentiability, and the existence of derivatives.
No, limit problems can only have one solution. The limit of a function is unique at a specific point, and it represents the exact value that the function is approaching. However, different methods can be used to arrive at the same limit value.