Find the limit of (x --> 0+) coth(x)

Question

lim (x --> 0+) coth(x)

 

I get :

 

2e⁰ + 2e^-0

_________

2e⁰ - 2e^-0

 

=  4/0

 

But you can't have a zero in the denominator. What have I done wrong?

 

#23(g), p263

ANSWER:   ∞

Answer 1

It is coming in from the right...instead of putting in 0 try putting in .0001.  See what happens to the bottom if it gets smaller and it is smaller than the numerator, the function will go to infinity.