2) is there a typo?
is the limit ((x+3)/x)^x?
Please, I need step by step solution of this two limits. I'd be so greatful for help. please don't mind my stupidity of not knowing L'Hospital rule...
So, this's killing me:
1. lim (x/x-1 - 1/ln x)
x->1
2. lim (x+3/x)^x
x->infinity
You can treat [(x+3)/x]^x=y
Of you ln both side, you will get:
ln (y)= x ln[(x+3)/x]
= [(x+3)/x] / (1/x)
Then you can apply L'hopital rule, that is differentiate the numerator and denominator separately
Eventually you will get:
lim{x to infinity} ln y = -3/(x+3)
= 0
lim{x to infinity} y = 1
lim{x to infinity} [(x+3)/x]^x=1
sorry, i do not know how to type the math notation.