Answer the questions below. Each response should be precise and mathematically accurate.
(i) Define the left–hand limit and the right–hand limit of a function f at a point a. Use limit notation in your definitions.
(ii) State the limit law for the quotient of two functions, clearly mentioning the condition under which it holds.
(iii) The natural logarithm function g(x)=lnx is defined only for x>0. Explain why this domain restriction is crucial when one computes x→0+limlnx. Your explanation should make explicit reference to the concept of a limit from the right.