The GATE Grind

GATE 2025 MT – Question 25

Engineering Mathematics · Calculus and vector calculus · 1 mark · Multiple select

Which of the following functions is/are expandable using Maclaurin series?

  1. $\ln(1+z)$
  2. $\ln z$
  3. $1/z^2$
  4. $\exp z$

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Correct answer: (A) $\ln(1+z)$; (D) $\exp z$

Explanation

A Maclaurin series is a Taylor expansion about zero and requires analyticity there. ln(1+z)=z−z²/2+… and exp(z)=1+z+z²/2+… satisfy this. ln z and 1/z² are singular at zero. Therefore **A,D**.