Just what is the question?Rayquesto said:Homework Statement
If lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1, then does this
=>
lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??
Homework Equations
lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1
The Attempt at a Solution
lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))] = ln(1)
A limit rule is a mathematical principle that describes the behavior of a function as its input approaches a certain value. It helps us understand the behavior of a function near a specific point, and can be used to evaluate limits and determine continuity.
The implication of a limit rule is that it allows us to make predictions about the behavior of a function without having to know the exact value at a specific point. This can be useful in many areas of mathematics and science, such as calculus, physics, and economics.
Limit rules are based on the concept of a limit, which is the value that a function approaches as its input approaches a certain value. The rules themselves are derived from the properties of limits, such as the sum, difference, product, and quotient rules.
Some common limit rules include the sum rule, difference rule, product rule, quotient rule, and power rule. These rules can be used to evaluate limits of various types of functions, such as polynomials, rational functions, exponential functions, and trigonometric functions.
Limit rules are important because they allow us to make predictions and solve problems involving the behavior of functions without having to know the exact value at a specific point. They are also essential in many areas of mathematics and science, and provide a foundation for more advanced concepts such as derivatives and integrals.