The GATE Grind

GATE 2014 EC (EC1) – Question 36

Engineering Mathematics · Calculus · 2 marks · Multiple choice

Find the Taylor expansion of $3\sin x+2\cos x$.

  1. $2+3x-x^2-x^3/2+\cdots$
  2. $2-3x+x^2-x^3/2+\cdots$
  3. $2+3x+x^2+x^3/2+\cdots$
  4. $2-3x-x^2+x^3/2+\cdots$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $2+3x-x^2-x^3/2+\cdots$

Explanation

Use sinx=x−x³/6+… and cosx=1−x²/2+…. Multiplying gives3sinx=3x−x³/2+… and2cosx=2−x²+…. Their sum is **2+3x−x²−x³/2+…,A**. The constant term comes entirely from the cosine.