Worksheet: Limits of Multivariable Functions

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()()𝑥𝑦4𝑦, if it exists.

Q3:

Evaluate lim()()𝑥𝑦, if it exists.

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

Q4:

Evaluate lim()()𝑥𝑦𝑥+𝑥𝑦+𝑦, if it exists.

Q5:

Evaluate the limit lim()()𝑥𝑦𝑦(𝑥1)+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()()𝑥4𝑦𝑥+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+𝑦𝑥+𝑦+11 if it exists.

Q11:

Evaluate limsin()𝑦(𝑥𝑦), 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()()𝑥2𝑥𝑦+𝑦𝑥𝑦, 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()()𝑥𝑦𝑥+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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