Limit solving without using series

[Mark J.]

Any way to solve the following limit without using series:

lim (3^x (3*(x^2)+2) / (7+x)! when x->infinity

Regards

 

[jfgobin]

You could start with Stirling's[/PLAIN] approximation.

 

[johnqwertyful]

You can easily squeeze that. 3*x^2+2<=3^x from some point on.