Evaluate the Limit?
#lim_(xrarr oo) [x(tan(2/x))] #
1 Answer
The limit is
Explanation:
We can rewrite as
#L = lim_(x-> oo) tan(2/x)/(1/x)#
We see that
#L = lim_(x->oo) (-2/x^2 * sec^2(2/x))/(-1/x^2)#
#L = lim_(x-> oo) 2sec^2(2/x)#
The same principal applies with
#L = 2sec^2(0)#
#L = 2(1)#
#L = 2#
A graphical verification confirms.
In the above graph, the red curve is
Hopefully this helps!