What happened to the ##\ln##?AlexandraMarie112 said:Homework Statement
Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3)
Homework Equations
The Attempt at a Solution
Ln(x^2-1)/(2x^2+3)
Then I divided the top and bottom by x^2 so in the end I got (1/2).
Is this right?
Yes that's what I did. So my final answer then should be Ln(1/2) ?Mastermind01 said:Is this what you did? :
##\lim_{n\rightarrow +\infty} {\ln {(x^2 - 1)} - \ln{(2x^2+3)}}##
## = \lim_{n\rightarrow +\infty} {\ln ({\frac{x^2 - 1}{2x^2+3}})}#### = {\ln {\lim_{n\rightarrow +\infty}(\frac{1 - \frac{1}{x^2}}{2+\frac{3}{x^2}}})}##
You got the limit of the inside part as ##\frac{1}{2}## you need to take its ##\ln## to get the right answer.
Right, or -ln(2)AlexandraMarie112 said:Yes that's what I did. So my final answer then should be Ln(1/2) ?
The "infinity limit with natural log" refers to the limit of a function as the input approaches infinity, where the function involves the natural logarithm.
The infinity limit with natural log is calculated by taking the limit of the function as x approaches infinity, and then evaluating the resulting expression using calculus or other mathematical methods.
The infinity limit with natural log is important in many areas of mathematics, including calculus, differential equations, and complex analysis. It is often used to model real-life situations and make predictions about the behavior of various systems.
Yes, the infinity limit with natural log can be negative. This can occur when the function approaches negative infinity as x approaches infinity, or when the function has a negative constant term in addition to the natural logarithm.
Yes, the infinity limit with natural log has many practical applications, including in physics, engineering, and economics. It can be used to model population growth, radioactive decay, and many other phenomena.