The GATE Grind

GATE 2016 CE (CE2) – Question 15

Engineering Mathematics · Calculus: Limits, continuity, mean value theorems, maxima and minima, Taylor series · 1 mark · Multiple choice

What is $\lim_{(x,y)\to(0,0)}xy/(x^2+y^2)$?

  1. 1
  2. −1
  3. 0
  4. Limit does not exist

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) Limit does not exist

Explanation

Along y=0, xy/(x²+y²)=0 for every nonzero x. Along y=x, the same expression equals1/2 for nonzero x. Since the limits depend on the approach path, no unique two-variable limit exists. Therefore **D**.