alexd
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Homework Statement
lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]
Homework Equations
hey guys, can anyone please help me solve this limit (without a calculator..)
10x!
The discussion revolves around evaluating the limit of the expression (sqrt(cosX) - cosX) / (x^2) as x approaches infinity. Participants are exploring the behavior of the function and its components as x increases without the use of a calculator.
The conversation is active, with participants sharing insights about the limit's behavior. There is an ongoing exploration of the relationship between the numerator and denominator, and some participants are questioning their assumptions about convergence.
There is a mention of confusion regarding the limit as x approaches zero versus infinity, and participants are clarifying the conditions under which the limit is being evaluated. The discussion includes considerations of the bounded nature of the cosine function.
alexd said:lim (x-->infinity) [(sqrt(cosX)-cosX)/(x^2)]
… you don't mean limx -> 0, do you?)alexd said:I drew the graph, it seems to be going to zero when x->∞
alexd said:The case for x->0 is much easier - the answer is 1/4...
is that what u meant?
ok.. I think I see where u're going with this...
so it's actually not defined when x->∞
alexd said:well...
the bottom obviously goes to ∞ when x->∞
and as for the top.. I have no idea...
that's where i got stuck the 1st time..
what do you do with cosx when x->∞?
