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I want to find the limit as t approaches infinity of the function u(x,t) using mathematica. Can someone please help me do this?

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    $\begingroup$ there is no limit. Because $\cos(t)$ has no limit as $t$ goes to infinity. You do not need Mathematica for this :) $\endgroup$ – Nasser Apr 9 at 22:33
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    $\begingroup$ I'm voting to close this question as off-topic because the issue it raises is not really a Mathematica issue but a matter of the OP not having grasped the relevant mathematics. $\endgroup$ – m_goldberg Apr 11 at 2:39
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As pointed out in the comments, this function has no limit. Indeed, the more transparent version:

Limit[Cos[t], t -> Infinity]

returns Indeterminate, as you might expect. While the limit does not exist, you can get bounds on the limit. For example,

MaxLimit[Cos[t], t -> Infinity]

and

MinLimit[Cos[t], t -> Infinity]

return 1 and -1. For a function of two variables, it's the same thing. For example,

MaxLimit[Cos[t] + Exp[-t] x, t -> Infinity]
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