Interesting question, you know that the dependent exemption no longer exists in 2018 right?  So are you asking about the child tax credit, or something else?

Technically it exists, but the amount is $0.  

Fortunately, the change to $0 does not affect other things, such as the threshold to claim a Qualifying Relative (which can potentially mean a $500 credit for the person claiming the dependent).

What I actually meant was - if a relative lived with me over half the year and meets all other qualifications up to how much the relative can earn then I can claim him. Last year the limit was the exemption amount. Since there is no exemption amount this year so how do I decide if I can claim him.
My understanding is the limit is $1050 plus $350.
Your input is appreciated in advance.

The language that you are using makes it very difficult to answer your questions.  A qualifying child must live with you for over half the year, but they do not have a gross income test - they just cannot provide over half of their own support.  A qualifying relative, either does not have to live you with you at all, or if not actually a relative, must live with you for all 12 months.  A qualifying relative cannot have a gross income more than $4,150 in 2018.

The limit that you posted is a tortured version of the standard deduction for dependents which is the higher of earned income + 350 or $1,050, but does not have anything to do with the gross income test for a qualifying relative.

Thank you, Tax Monkey, your answer has clarified all my doubts. I very much appreciate the way you explained.