Calculate Limit of 3/ (x (ln (x+4) - ln (x)) as x→∞

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Homework Help Overview

The problem involves calculating the limit of the expression 3 / (x (ln (x+4) - ln (x))) as x approaches infinity, which falls under the subject area of calculus, specifically limits and logarithmic functions.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to reason through the limit by considering the behavior of the denominator as x increases, initially suggesting it approaches zero. They also explore the transformation of the logarithmic expression. Other participants question the conclusion of infinity and suggest that the limit approaches a positive number instead.

Discussion Status

The discussion is ongoing, with participants providing hints and clarifications regarding the logarithmic properties and the behavior of the limit. There is no explicit consensus, but some guidance has been offered regarding the nature of the limit.

Contextual Notes

Participants are navigating assumptions about the behavior of logarithmic functions and limits as x approaches infinity, with some uncertainty about the implications of their transformations.

intenzxboi
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Homework Statement



3/ (x (ln (x+4) - ln (x))

as x goes to infinity.

so first i look at this i i thought its going to 0 cause x is going to get larger at the bottom.

but then i see that the equation looks more like 3 / (x( ln ((x+1)/x))
ln ((x+1)/x) is going to 1. so that mean that ln 1= 0

so...
3 / x(0) = infinty?
 
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Nope, not infinity.

Hint: ln(a) - ln(b) = ln(a/b) and (1 + a/x)x → ea as x → ∞
 
it doesn't go to zero?
 
No. The limit is a positive number.
 
Last edited:

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