Texas Rules of Evidence Rule 105. Limited Admissibility

(a) Limiting Instruction. When evidence which is admissible as to one party or for one purpose but not admissible as to another party or for another purpose is admitted, the court, upon request, shall restrict the evidence to its proper scope and instruct the jury accordingly; but, in the absence of such request the court’s action in admitting such evidence without limitation shall not be a ground for complaint on appeal.

(b) Offering Evidence for Limited Purpose. When evidence referred to in paragraph (a) is excluded, such exclusion shall not be a ground for complaint on appeal unless the proponent expressly offers the evidence for its limited, admissible purpose or limits its offer to the party against whom it is admissible.