Worksheet: Limits of Multivariable Functions

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In this worksheet, we will practice finding the limit of multivariable functions as we approach a point in the domain of the function.

Q1:

Evaluate the limit limsin()→()𝑦𝑥𝑥+𝑦, if it exists.

  • AThe limit does not exist.
  • B 1 2
  • C0

Q2:

Evaluate lim()→()𝑥𝑦−4𝑦, if it exists.

Q3:

Evaluate lim()→()𝑥𝑦, if it exists.

  • AThe limit does not exist.
  • B1
  • C − 1
  • D0

Q4:

Evaluate lim()→()𝑥−𝑦𝑥+𝑥𝑦+𝑦, if it exists.

Q5:

Evaluate the limit lim()→()𝑥𝑦−𝑦(𝑥−1)+𝑦, if it exists.

  • A0
  • B 1 2
  • CThe limit does not exist.

Q6:

Evaluate the limit lim()→()𝑥𝑦𝑥+𝑦, if it exists.

  • A1
  • BThe limit does not exist.
  • C 1 2
  • D0

Q7:

Evaluate lim()→()𝑥𝑦𝑥+𝑦, if it exists.

Q8:

Evaluate lim()→()𝑥−4𝑦𝑥+2𝑦, if it exists.

  • A − 2
  • B − 4 3
  • CThe limit does not exist.
  • D0

Q9:

Evaluate lim()→()𝑥𝑦𝑧𝑥+𝑦+𝑧, if it exists.

Q10:

Evaluate the limit lim()→()𝑥+𝑦√𝑥+𝑦+1−1 if it exists.

Q11:

Evaluate limsin()→𝑦(𝑥−𝑦), if it exists.

  • A 𝜋 2
  • BThe limit does not exist.
  • C − 𝜋
  • D0

Q12:

Evaluate limcos()→()1𝑥𝑦, if it exists.

  • A1
  • B0
  • C − 1
  • DThe limit does not exist.

Q13:

Evaluate the limit limcos()→()𝑥+𝑦1𝑥𝑦, if it exists.

  • A1
  • BThe limit does not exist.
  • C 1 2

Q14:

Evaluate limcos()→()𝑥𝑦𝑦𝑥+𝑦,if it exists.

  • A 4 𝜋
  • B 1 2
  • C1
  • DThe limit does not exist.
  • E0

Q15:

Evaluate limcos()→()5𝑦𝑥𝑥+𝑦 if it exists.

  • A5
  • BThe limit does not exist.
  • C0
  • D 5 2

Q16:

Evaluate lim()→()𝑒, if it exists.

Q17:

Evaluate the limit lim()→()√𝑒, if it exists.

  • A 𝑒 √
  • B 𝑒
  • CThe limit does not exist.
  • D 𝑒
  • E 𝑒 √

Q18:

Evaluate limtan()→𝑒𝑥𝑧, if it exists.

  • AThe limit does not exist.
  • B0
  • C √ 3

Q19:

Evaluatelimcos()→()𝑥𝑦 if it exists.

Q20:

Evaluate lim()→()𝑥𝑦𝑥+𝑦, if it exists.

Q21:

Evaluate lim()→()𝑥−2𝑥𝑦+𝑦𝑥−𝑦, if it exists.

Q22:

Evaluate the limit lim()→()𝑥𝑦𝑥+𝑦, if it exists.

  • A0
  • B 1 2
  • C − 1 2
  • DThe limit does not exist.

Q23:

Evaluate the limit limsin()→()𝑦𝑥𝑦𝑥+𝑦, if it exists.

Q24:

Evaluate the limit lim()→()𝑥−𝑦𝑥+𝑦, if it exists.

  • A − 1
  • B0
  • C1
  • DThe limit does not exist.

Q25:

Evaluate lim()→()𝑥𝑦𝑥+𝑦, if it exists.

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