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GATE 2022 MT – Question 11

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

The Taylor series of $f(x)=(x+1)/(e^x+1)$ about $x=0$, truncated to its first two terms, is

  1. $1/2+x/4$
  2. $1/2+x/2$
  3. $1/2+x$
  4. $1/2+2x$

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Show answer and explanation

Correct answer: (A) $1/2+x/4$

Explanation

At zero, $f(0)=1/2$. Quotient differentiation gives $f^\prime(0)=[2-1]/4=1/4$. The truncated series is $1/2+x/4$, **A**.