A rational function is defined by L(x)= x+7 -3 x^ 2 -4

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

Problem

A rational function is defined by L(x)=x+7−3x2−4.L(x)=\frac{\sqrt{x+7}-3}{x^{2}-4}. Throughout this problem, xx is assumed to be close to 22 but not equal to 22. (1) Rewrite L(x)L(x) into an algebraically equivalent form that does not contain a radical expression in the numerator and clearly exhibits all factors that may cancel. Show every intermediate algebraic step. (2) Using the expression obtained in part (a), determine lim⁡x→2L(x)\displaystyle \lim_{x\to 2}L(x). Give a brief justification for each step leading to the numerical value.

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