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2022 PEA Q21

lim⁡x→eln⁡x−1x−e\displaystyle \lim_{x \to e} \frac{\ln x - 1}{x - e}.

Reveal answer and solution

Answer

C

Solution

  1. 1

    This is the definition of ddx(ln⁡x)\dfrac{d}{dx}(\ln x) at x=ex = e:

  2. 2
    lim⁡x→eln⁡x−ln⁡ex−e=1e. \lim_{x \to e} \frac{\ln x - \ln e}{x - e} = \frac{1}{e}.

Answer structure / marking notes

Recognize the limit as a derivative; no algebra required.

Content note

Imported from public/resources/isi/msqe/solutions/pea/2022/ISI_MSQE_PEA_2022_Solutions.tex. Question wording is retained from the available local TeX source; incomplete option blocks or ambiguous source status are flagged for review.