How to evaluate these Limits

lim ln(sin(x^2+y^2))
(x,y)->(0,0)

lim (x - ln(coshx))
x->infinite

Please give full working.

1. When (x,y) -->(0,0), x^2 + y^2 --> 0 from the right ==> ln(sin(x^2 + x^2) --> -- oo

2.
cosh(x) = (e^x + e^(-x))/2 = e^x(1 + e^(-2x))/2

==> ln(cosh x) = x + ln(1 + e^(-2x)) - ln(2)

==> x - ln(cosh(x)) = ln(2) - ln(l+ e^(-2x))

As x --> oo, 1 + e^(-2x) --> 1 ==> ln(1 + e^(-2x)) --> ln(1) = 0

Conclusion: lim (x --> oo) [x - ln cosh(x)] = ln(2) + 0 = ln(2)