The functions and are defined for near

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

Problem

The functions pp and qq are defined for xx near 22. Selected values of each function are shown. Numerical data for pp:
x1.81.91.992.012.12.2
p(x)4.244.094.00093.99913.913.76
Numerical data for qq:
x1.81.91.992.012.12.2
q(x)−1.56−1.42−1.2009−1.1991−1.12−1.02
Use the information in the tables to analyze the behavior of pp and qq as xx approaches 22. (a) Estimate lim⁡x→2p(x)\displaystyle\lim_{x\to 2}p(x) and lim⁡x→2q(x)\displaystyle\lim_{x\to 2}q(x), providing numerical evidence from the tables. (b) Determine whether lim⁡x→2(p(x)+q(x))\displaystyle\lim_{x\to 2}\bigl(p(x)+q(x)\bigr) exists. If it exists, approximate its value and justify your conclusion using appropriate limit reasoning. (c) Describe, in complete sentences, how the limits you obtained in part (a) support the existence or non-existence of the limit you considered in part (b).

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