For a real parameter

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For a real parameter kk, consider the family of functions fk(x)=kx4+3x2−22x4−k.f_k(x)=\frac{kx^{4}+3x^{2}-2}{2x^{4}-k}. (1) Part (a) — Formula for L(k)L(k) (2) Part (b) — Sign analysis and existence of limit (3) Part (c) — Parameter values producing L(k)=12L(k)=\tfrac12

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