- #1
daveronan
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Homework Statement
Find the limit of the following function
lim w→∞ (1 + z/w)w
Homework Equations
The Attempt at a Solution
lim w→∞ w ln(1 + z/w)
Not sure where to go next...
Thanks
Dick said:w ln(1 + z/w) has the form infinity*0. You'll want to arrange it into an infinity/infinity form before you do l'Hopital. Can you show how you tried to apply it?
daveronan said:lim w→∞ w.ln(1/w*(w+z))
daveronan said:After l'Hopital I'm getting lim w → ∞ ( -z/(w+z) + ln(1 + z/w))
This doesn't seem to help, not unless I'm doing something stupid.
A limit is a fundamental concept in calculus that describes the behavior of a function as the input approaches a certain value. It is denoted by the symbol "lim" and is used to determine the value that a function is approaching as the input gets closer and closer to a specific value.
To find the limit of a function, you can use three different methods: substitution, factoring, and rationalization. These methods involve plugging in the value the function is approaching, simplifying the resulting expression, and evaluating it to determine the limit.
The limit of a function is important because it helps us understand the behavior of a function and its graph. It also allows us to evaluate functions that are undefined at certain points and to solve various problems in physics, economics, and other fields that involve continuous change.
No, you cannot find the limit of a function at a discontinuity because the function is not defined at that point. In order to find the limit, the function must be defined and continuous at the point of interest.
You can check your answer by plugging in nearby values to the limit point and seeing if the resulting values are approaching the same limit. You can also use a graphing calculator or online graphing tool to visualize the behavior of the function and confirm your answer.