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GATE 2020 ST – Question 14

Calculus · Multivariable Calculus · 1 mark · Multiple choice

For (x,y)≠(0,0), $f=(4x^2+9y^2)/(\sqrt{4x^2+9y^2+64}-8)$; set f(0,0)=c. Which is true?

  1. No c makes f continuous at the origin.
  2. Continuous if c=0.
  3. Continuous if c=10.
  4. Continuous if c=16.

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Show answer and explanation

Correct answer: (D) Continuous if c=16.

Explanation

Multiply numerator and denominator by the conjugate. Away from zero, the expression becomes √(4x²+9y²+64)+8, whose limit is8+8=16. Defining the origin value as16 makes the function continuous. Therefore D.

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