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 rij(๐‘ก)=(5๐‘ก)+(5๐‘ก)cossin.

  • A
  • B
  • C
  • D
  • E

Q2:

Sketch the graph of the vector-valued function rij(๐‘ก)=(3๐‘ก)+๏€ผ94๐‘ก๏ˆ๏Šจ.

  • A
  • B
  • C
  • D
  • E

Q3:

Find the domain of the vector-valued function rijk(๐‘ก)=๏€ฟ1โˆš2๐‘กโˆ’4๏‹+(2๐‘ก)+((๐‘กโˆ’1))cscln.

  • A๐‘ก>2,๐‘กโ‰ ๐‘›๐œ‹, where ๐‘› is an integer number
  • B๐‘ก>2
  • C๐‘ก>4
  • D๐‘ก>4,๐‘กโ‰ ๐‘›๐œ‹, where ๐‘› is an integer number
  • E๐‘กโ‰ฅ2,๐‘กโ‰ ๐‘›๐œ‹, where ๐‘› is an integer number

Q4:

Sketch the graphs of the vector-valued function rij(๐‘ก)=(๐‘ก)+(๐‘ก)๏Šฉ.

  • A
  • B
  • C
  • D
  • E

Q5:

For the given function rijk(๐‘ก)=2๐‘’+(๐‘ก๐œ‹)โˆ’(๐‘ก)๏๏Šฑ๏Šงcosln, evaluate r(1).

  • A2โˆ’ij
  • B2+ij
  • C2
  • D3
  • E2+ik

Q6:

For the given function rij(๐‘ก)=๏€น๐‘กโˆ’1๏…+๐‘ก๏Šจ, find rr(๐‘กโˆ’1)โˆ’(๐‘ก).

  • Aโˆ’2๐‘ก
  • B(โˆ’2๐‘ก+1)โˆ’ij
  • C(๐‘ก+2)โˆ’ij
  • D(โˆ’2๐‘ก+2)โˆ’ij
  • E๐‘ก+1

Q7:

Find the domain of the vector-valued function rijk(๐‘ก)=๏€น๐‘ก+4๏…+(๐‘ก)+2(๐‘ก)๏Šจtanln.

  • A๐‘ก>0, ๐‘กโ‰ ๐œ‹2๐‘›, where ๐‘› is an integer
  • B๐‘ก>0, ๐‘กโ‰ (2๐‘›+1)๐œ‹2, where ๐‘› is an integer
  • C๐‘ก>0, ๐‘กโ‰ (2๐‘›+1)๐œ‹4, where ๐‘› is an integer
  • D๐‘กโ‰ฅ0, ๐‘กโ‰ (2๐‘›+1)๐œ‹2, where ๐‘› is an integer
  • E๐‘กโ‰ฅ0, ๐‘กโ‰ (2๐‘›+1)๐œ‹, where ๐‘› is an integer

Q8:

For the given function rij(๐‘ก)=2(2๐‘ก)+3(๐‘ก)csctan, evaluate r๏€ป๐œ‹4๏‡.

  • Aij+
  • B5
  • C2
  • D2+3ij
  • Eโˆ’2+3ij

Q9:

For the given function ๐‘Ÿ(๐‘ก)=2๐‘ก๐‘–+๏€น2๐‘ก+3๏…๐‘—๏Šจ, evaluate ๐‘Ÿ(0).

  • A3๐‘—
  • B3
  • C5
  • D3๐‘–
  • E๐‘–+3๐‘—

Q10:

Find the domain of the vector-valued function rijk(๐‘ก)=๏€น2๐‘ก๏…+๏€ปโˆš๐‘กโˆ’1๏‡+๏€ผ52๐‘ก+4๏ˆ๏Šจ.

  • A๐‘…โˆ’{โˆ’2}
  • B[โˆ’2,โˆž)
  • C๐‘…
  • D[1,โˆž)
  • E(1,โˆž)

Q11:

For the vector-valued function r(๐‘ก)=๏š๐‘ก+47๐‘กโˆ’54๐‘กโˆ’2๐‘ก๏ฆ,๏Šจ๏Šฉ evaluate r(โˆ’3).

  • A๏˜1326102๏ค
  • B131
  • Cโˆ’115
  • D๏˜1316โˆ’87๏ค
  • E๏˜13โˆ’26โˆ’102๏ค

Q12:

Which of the following vector-valued equations is represented by the graph shown below?

  • Ar(๐‘ก)=๏š๐‘ก(๐‘ก)(๐‘ก)๏ฆsincos
  • Br(๐‘ก)=๏š๐‘ก(๐‘ก)๐‘ก(๐‘ก)๐‘ก๏ฆsincos
  • Cr(๐‘ก)=๏š(๐‘ก)(๐‘ก)๐‘ก๏ฆsincos
  • Dr(๐‘ก)=๏š๐‘ก(๐‘ก)๐‘ก(๐‘ก)๐‘ก๏ฆcossin
  • Er(๐‘ก)=๏š(๐‘ก)(๐‘ก)๐‘ก๏ฆcossin

Q13:

Identify the graph of the vector-valued function rijk(๐‘ก)=๏€น๐‘’(5๐‘ก)๏…+๏€น๐‘’(5๐‘ก)๏…+๐‘’๏Šฑ๏๏Šฑ๏๏Šฑ๏sincos.

  • A
  • B
  • C
  • D
  • E

Q14:

Find the domain of the vector-valued function rijk(๐‘ก)=(๐‘ก)+๏€ปโˆš3๐‘ก+2๏‡+15โˆ’๐‘กsec.

  • A๐‘กโ‰ฅโˆ’23, ๐‘กโ‰ 5, and ๐‘กโ‰ ๏€ผ2๐‘›+12๏ˆ๐œ‹, where ๐‘› is an integer.
  • B๐‘ก>โˆ’23, ๐‘กโ‰ 5, and ๐‘กโ‰ ๐‘›๐œ‹, where ๐‘› is an integer.
  • C๐‘กโ‰ โˆ’32, ๐‘กโ‰ฅโˆ’5, and ๐‘กโ‰ ๏€ผ2๐‘›+12๏ˆ๐œ‹, where ๐‘› is an integer.
  • D๐‘กโ‰ฅโˆ’23, ๐‘กโ‰ โˆ’5, and ๐‘กโ‰ ๐‘›๐œ‹, where ๐‘› is an integer.
  • E๐‘กโ‰ฅ23, ๐‘กโ‰ โˆ’5, and ๐‘กโ‰ ๏€ผ2๐‘›+12๏ˆ๐œ‹, where ๐‘› is an integer.

Q15:

Sketch the graph of the vector-valued function rij(๐‘ก)=๐‘ก+๐‘กcos.

  • A
  • B
  • C
  • D
  • E

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