Limit lim(x->pi/4) tan(2x) =tan(pi/2)

[bard]

lim(x->pi/4) tan(2x) =tan(pi/2) wat to do after this, it is undefined

 

[whozum]

tan(pi/2) is undefined but the limit is not. take a look at a graph of tan(x) and see what's going on just to the left or right of pi/2.

 

[LeonhardEuler]

Actually the limit is not defined. As x approaches \frac{\pi}{2} from the left, the function approaches infinity. As x approaches from the right, the function approaches negative infinity. The limit from the left does not equal the limit from the right, so the limit does not exist. Actually, strictly speaking, the limit would not exist even if the function approached positive infinty from both sides, since the definition of the limit requires that the function get arbitrarily close to the limit, and it is impossible for a function to be within some definite value of infinty.