Worksheet: Properties of Limits

In this worksheet, we will practice using the properties of limits such as the limits of sums, differences, products, and quotients of functions and the limit of composite functions.

Q1:

If lim𝑓(𝑥)+9𝑥4=2, find lim𝑓(𝑥).

Q2:

Given that lim𝑓(𝑥)3𝑥=3, determine lim𝑓(𝑥).

Q3:

Consider the graphs of the functions 𝑓(𝑥) and 𝑔(𝑥).

Find lim𝑓(𝑥)+𝑔(𝑥).

  • A5
  • B2
  • C7
  • D3
  • E2

Q4:

Assume that lim𝑓(𝑥)=5. Find lim(𝑥+2)𝑓(𝑥).

Q5:

Assuming that lim(𝑥)=3, find lim𝑥(𝑥).

Q6:

Given that lim6𝑓(𝑥)+4𝑥+1=4, find lim𝑓(𝑥).

Q7:

Consider the graph of 𝑓(𝑥).

Find lim(𝑥𝑓(𝑥)).

Q8:

Assume that lim𝑓(𝑥)=3 and lim𝑔(𝑥)=8. Find lim𝑔(𝑥)𝑓(𝑥).

  • A11
  • B5
  • C6
  • D11
  • E5

Q9:

Assume that lim𝑓(𝑥)=5, lim𝑔(𝑥)=8, and lim(𝑥)=9. Find lim(𝑓(𝑥)𝑔(𝑥)(𝑥)).

Q10:

Given that lim𝑓(𝑥)4𝑥=4, determine lim𝑓(𝑥)𝑥.

Q11:

Consider the graph of 𝑓(𝑥).

Find lim(2𝑥𝑓(𝑥)).

Q12:

Given that lim2𝑓(𝑥)=4, find lim𝑓(𝑥).

  • A8
  • B4
  • C4
  • D64
  • E16

Q13:

If 𝑔(𝑥)=𝑓(𝑥)+1 and lim𝑓(𝑥)=2, determine lim𝑔(𝑥)𝑓(𝑥).

  • A2
  • B52
  • C72
  • D5
  • E32

Q14:

If 𝑔(𝑥)=2𝑓(𝑥) and lim𝑔(𝑥)𝑥+1=6, determine lim𝑓(𝑥).

  • A60
  • B15
  • C52
  • D30
  • E9

Q15:

Given that lim𝑓(𝑥)+𝑥=10, determine lim𝑓(𝑥).

  • A6
  • B6
  • C2
  • D14
  • E14

Q16:

If lim𝑓(𝑥)+𝑥=9, determine lim𝑓(𝑥)1.

  • A6
  • B10
  • C7
  • D2
  • E6

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