lim x->+∞ ( [(π/2)- arctg(1/t^3)]?
This limit comes from a given integral from 1 to x.
My teacher said that the limit (in the title) is +∞. Because it's like a rectangle with unlimited basis and height= π/2.
(And the limit to -∞ is -∞). Why does using the direct substitution should be wrong? It would be equal to [π/2- arctg(0)]= π/2. Why is this wrong?
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lim x-->inf ( pi/2 - arctan(1/x^3))
= lim x-->inf pi/2 - lim x-->inf arctan(x^(-3))
= pi/2 - lim x-->inf arctan(x^(-3))
= pi/2 - arctan(lim x-->inf 1/x^3)
= pi/2 - 0
= pi/2
Note:
t has been replaced by x
There are numerous things wrong in the title.
First off, we dont have the original/complete question.
Second, in ur title, you say lim x --> ∞ but in your expression [(π/2)- arctg(1/t^3) there is no "x". But there is a "t".
Fix all that so ur question makes sense and we can take it from there...