Suppose and . Which one of the following statements is always…

MATHEMATICS · Single correct · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

Suppose lim⁡x→2p(x)=5\lim_{x\to 2}p(x)=5 and lim⁡x→2q(x)=−3\lim_{x\to 2}q(x)=-3. Which one of the following statements is always true? (a) lim⁡x→2[p(x)+q(x)]=2\displaystyle\lim_{x\to 2}[p(x)+q(x)]=2 (b) lim⁡x→2[p(x)−q(x)]=2\displaystyle\lim_{x\to 2}[p(x)-q(x)]=2 (c) lim⁡x→2p(x)q(x)=−15\displaystyle\lim_{x\to 2}\dfrac{p(x)}{q(x)}=-15 (d) lim⁡x→2[p(x)+q(x)]=8\displaystyle\lim_{x\to 2}[p(x)+q(x)]=8

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