We may split the limit up as follows, recalling the fact that
lim_(x->a)[f(x)+-g(x)]=lim_(x->a)f(x)+-lim_(x->a)g(x)
Then,
lim_(x->0^+)(1+1/x)=lim_(x->0^+)1+lim_(x->0^+)1/x
lim_(x->0^+)1=1, in general, the limit to any value of a constant is simply that constant.
To determine lim_(x->0^+)1/x, envision dividing 1/x by smaller and smaller positive numbers, as we're approaching 0 from the positive side:
1/0.1=10
1/0.01=100
1/0.001=1000
1/0.0001=10000
We can see as we approach 0 from the positive side, our result gets larger and larger, that is, heads toward oo.
Thus, lim_(x->0^+)1/x=oo
Our result is
lim_(x->0^+)(1+1/x)=1+oo=oo, the 1 doesn't change the fact that we're heading toward infinity, it doesn't impact the answer, 1 is insignificant in comparison.