Question

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

Answer 1

Any ideas?

Answer 2

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

Answer 3

are you sure the put the right attachment

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Ah, I see, thats kind of a strange problem

Answer 11

thanks!