Worksheet: Vector-Valued Functions

In this worksheet, we will practice defining, evaluating and graphing vector-valued functions.

Q1:

Sketch the graphs of the vector-valued function 𝑟 ( 𝑡 ) = ( 5 𝑡 ) 𝑖 + ( 5 𝑡 ) 𝑗 c o s s i n .

  • A
  • B
  • C
  • D
  • E

Q2:

Sketch the graph of the vector-valued function r i j ( 𝑡 ) = ( 3 𝑡 ) + 9 4 𝑡 .

  • A
  • B
  • C
  • D
  • E

Q3:

Find the domain of the vector-valued function r i j k ( 𝑡 ) = 1 2 𝑡 4 + ( 2 𝑡 ) + ( ( 𝑡 1 ) ) c s c l n .

  • A 𝑡 > 4 , 𝑡 𝑛 𝜋 , where 𝑛 is an integer number
  • B 𝑡 > 4
  • C 𝑡 > 2 , 𝑡 𝑛 𝜋 , where 𝑛 is an integer number
  • D 𝑡 > 2
  • E 𝑡 2 , 𝑡 𝑛 𝜋 , where 𝑛 is an integer number

Q4:

Sketch the graphs of the vector-valued function r i j ( 𝑡 ) = ( 𝑡 ) + ( 𝑡 ) .

  • A
  • B
  • C
  • D
  • E

Q5:

For the given function 𝑟 ( 𝑡 ) = 2 𝑒 𝑖 + ( 𝑡 𝜋 ) 𝑗 ( 𝑡 ) 𝑘 c o s l n , evaluate 𝑟 ( 1 ) .

  • A3
  • B 2 𝑖 + 𝑗
  • C2
  • D 2 𝑖 𝑗
  • E 2 𝑖 + 𝑘

Q6:

For the given function 𝑟 ( 𝑡 ) = 𝑡 1 𝑖 + 𝑡 𝑗 , find 𝑟 ( 𝑡 1 ) 𝑟 ( 𝑡 ) .

  • A 𝑡 + 1
  • B ( 𝑡 + 2 ) 𝑖 𝑗
  • C ( 2 𝑡 + 1 ) 𝑖 𝑗
  • D ( 2 𝑡 + 2 ) 𝑖 𝑗
  • E 2 𝑡

Q7:

Find the domain of the vector-valued function 𝑟 ( 𝑡 ) = 𝑡 + 4 𝑖 + ( 𝑡 ) 𝑗 + 2 ( 𝑡 ) 𝑘 t a n l n .

  • A 𝑡 > 0 , 𝑡 ( 2 𝑛 + 1 ) 𝜋 2 , where 𝑛 is an integer
  • B 𝑡 > 0 , 𝑡 𝜋 2 𝑛 , where 𝑛 is an integer
  • C 𝑡 0 , 𝑡 ( 2 𝑛 + 1 ) 𝜋 2 , where 𝑛 is an integer
  • D 𝑡 > 0 , 𝑡 ( 2 𝑛 + 1 ) 𝜋 4 , where 𝑛 is an integer
  • E 𝑡 0 , 𝑡 ( 2 𝑛 + 1 ) 𝜋 , where 𝑛 is an integer

Q8:

For the given function 𝑟 ( 𝑡 ) = 2 ( 2 𝑡 ) 𝑖 + 3 ( 𝑡 ) 𝑗 c s c t a n , evaluate 𝑟 𝜋 4 .

  • A2
  • B 2 𝑖 + 3 𝑗
  • C5
  • D 2 𝑖 + 3 𝑗
  • E 𝑖 + 𝑗

Q9:

For the given function 𝑟 ( 𝑡 ) = 2 𝑡 𝑖 + 2 𝑡 + 3 𝑗 , evaluate 𝑟 ( 0 ) .

  • A 3 𝑗
  • B 3 𝑖
  • C3
  • D 𝑖 + 3 𝑗
  • E5

Q10:

Find the domain of the vector-valued function 𝑟 ( 𝑡 ) = 2 𝑡 𝑖 + 𝑡 1 𝑗 + 5 2 𝑡 + 4 𝑘 .

  • A 𝑅
  • B [ 2 , )
  • C 𝑅 { 2 }
  • D ( 1 , )
  • E [ 1 , )

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