## anonymous 4 years ago Is this a contradiction? On this problem they ask: Use the definitions of the hyperbolic functions to find the following limit: lim x->infinity sinhx However the answer is either: lim x->0^- coth(x) = -infinity or lim x->0^+ coth(x) = infinity Anyone see what I'm doing wrong? I'm attaching the original problem

1. anonymous

2. anonymous

Any ideas?

3. anonymous

i'm not sure what you're asking...

4. anonymous

are you sure the put the right attachment

5. anonymous

I'm sorry, my bad, mistyped the uploaded file

6. anonymous

I'll take that as no one is sure what to do...

7. anonymous

do you know the standard algebraic expressions for the hyperbolic functions?

8. anonymous

x = sinh x = (e^x - e^-x)/2

9. anonymous

* sinhx = sinh x = (e^x - e^-x)/2

10. campbell_st

well use the definition $\sinh (x) = (e^x - e^(-x))/2$ so its the $\lim_{x \rightarrow \infty} (e^x - e^(-x))/2$ rewriting $\lim_{x \rightarrow \infty} e^x/2 - \lim_{x \rightarrow \infty} 1/(2e^x)$ 2nd part approaches 0 as x approaches infinity 1st part has approaches infinity

11. anonymous

Ah, I see, thats kind of a strange problem

12. anonymous

thanks!