- #1
Cacophony
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Homework Statement
lim (lnx)^2/x
x-->infinity
Homework Equations
none
The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
=5/(x/lnx)
How do I calculate x/lnx?
Cacophony said:The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
=5/(x/lnx)
How do I calculate x/lnx?
Where did the 5 come from? In fact, where did any of this come from? What you have makes zero sense to me.Cacophony said:Homework Statement
lim (lnx)^2/x
x-->infinity
Homework Equations
none
The Attempt at a Solution
=5lnx/x * (1/lnx)/(1/lnx)
Cacophony said:=5/(x/lnx)
How do I calculate x/lnx?
Cacophony said:Homework Statement
lim (lnx)^2/x
x-->infinity
The limit of ln as x goes to infinity is infinity. This means that as x approaches infinity, the value of ln(x) also approaches infinity.
To calculate the limit of ln as x goes to infinity, you can use the L'Hopital's Rule or the properties of limits. For example, if the limit is in the form of ln(x)/x, you can rewrite it as 1/x and then take the limit as x approaches infinity.
The natural logarithm function, ln(x), is an increasing function, which means that as x increases, the value of ln(x) also increases. As x approaches infinity, the value of ln(x) will continue to increase without bound, meaning it has no finite limit.
No, the limit of ln as x goes to infinity cannot be negative. Since the natural logarithm function is always positive for positive values of x, the limit as x approaches infinity will also be positive or infinity.
Yes, the graph of ln(x) can help visualize the limit of ln as x goes to infinity. As x approaches infinity, the graph of ln(x) will continue to increase without bound in the positive direction.