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Worksheet: The Net Change Theorem

Q1:

True or False? The Net Change Theorem says that ο„Έ √ π‘₯ π‘₯ = √ 9 βˆ’ √ 4 9 4 d .

  • Afalse
  • Btrue

Q2:

True or False: If 𝑔 ( 𝑑 ) represents the rate of change of a cat’s weight in kilograms per month when it is 𝑑 months old, then ο„Έ 𝑔 ( 𝑑 ) 𝑑 4 0 d equals the cat’s weight when it is 4 months old.

  • Afalse
  • Btrue

Q3:

True or False: The net change theorem states that ο„Έ π‘₯ √ 𝑑 𝑑 = √ π‘₯ βˆ’ √ π‘Ž π‘₯ π‘Ž d d d .

  • AFalse
  • BTrue

Q4:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 5 𝑑 βˆ’ 3 2 . What distance does it travel between 𝑑 = 2 and 𝑑 = 4 ?

  • A 2 m
  • B 31 m
  • C 4 3 m
  • D 7 m

Q5:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 5 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 1 ?

  • A 2 m
  • B 1 1 0 m
  • C 1 2 m
  • D 1 3 1 0 m
  • E 7 1 0 m

Q6:

Suppose that 𝐹 ( 𝑑 ) = 𝑑 2 . Evaluate ο„Έ 𝐹 β€² ( 𝑑 ) 𝑑 3 1 d using the net change theorem.

Q7:

An oil tanker leaks at the rate π‘Ÿ = 𝑓 ( 𝑑 ) cubic litres per minute, where 𝑑 is minutes after the accident. Write an integral that expresses the volume of oil leaked out in the first hour.

  • A ο„Έ 𝑓 ( 𝑑 ) 𝑑 6 0 0 β€² d
  • B ο„Έ 𝑓 ( 𝑑 ) 𝑑 1 0 d
  • C ο„Έ 𝑓 ( 𝑑 ) 𝑑 1 0 β€² d
  • D ο„Έ 𝑓 ( 𝑑 ) 𝑑 6 0 0 d
  • E ο„Έ 𝑓 ( 𝑑 ) 𝑑 6 0 1 β€² d

Q8:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 𝑑 βˆ’ 5 2 . What distance does it travel between 𝑑 = 1 and 𝑑 = 4 ?

  • A 9 m
  • B 2 4 3 4 m
  • C 9 2 m
  • D 6 3 4 m

Q9:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 𝑑 βˆ’ 5 2 . What distance does it travel between 𝑑 = 1 and 𝑑 = 3 ?

  • A 3 1 3 m
  • B 9 4 m
  • C 1 9 1 2 m
  • D 7 9 1 2 m
  • E 1 4 3 m

Q10:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 4 𝑑 βˆ’ 1 . What distance does it travel between 𝑑 = 0 and 𝑑 = 2 ?

  • A 14 m
  • B 3 2 m
  • C 6 m
  • D 2 5 4 m
  • E 3 1 4 m

Q11:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 5 ?

  • A 35 m
  • B 4 m
  • C 10 m
  • D 2 9 2 m
  • E 4 1 2 m

Q12:

A particle’s velocity in metres per second as a function of time is 𝑣 ( 𝑑 ) = 2 𝑑 βˆ’ 3 . What distance does it travel between 𝑑 = 0 and 𝑑 = 4 ?

  • A 20 m
  • B 2 m
  • C 4 m
  • D 1 7 2 m
  • E 2 3 2 m