Worksheet: Properties of Limits

In this worksheet, we will practice using the properties of limits such as the limits of sum, difference, product, and quotient of functions and the limit of composite functions.

Q1:

If l i m 𝑓 ( 𝑥 ) + 9 𝑥 4 = 2 , find l i m 𝑓 ( 𝑥 ) .

Q2:

Given that l i m 𝑓 ( 𝑥 ) 3 𝑥 = 3 , determine l i m 𝑓 ( 𝑥 ) .

Q3:

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

Find l i m 𝑓 ( 𝑥 ) + 𝑔 ( 𝑥 ) .

  • A2
  • B 5
  • C 2
  • D 7
  • E 3

Q4:

Assume that l i m 𝑓 ( 𝑥 ) = 5 . Find l i m ( 𝑥 + 2 ) 𝑓 ( 𝑥 ) .

Q5:

Assuming that l i m ( 𝑥 ) = 3 , find l i m 𝑥 ( 𝑥 ) .

Q6:

Given that l i m 6 𝑓 ( 𝑥 ) + 4 𝑥 + 1 = 4 , find l i m 𝑓 ( 𝑥 ) .

Q7:

Consider the graph of 𝑓 ( 𝑥 ) .

Find l i m ( 𝑥 𝑓 ( 𝑥 ) ) .

Q8:

Assume that l i m 𝑓 ( 𝑥 ) = 3 and l i m 𝑔 ( 𝑥 ) = 8 . Find l i m 𝑔 ( 𝑥 ) 𝑓 ( 𝑥 ) .

  • A5
  • B 5
  • C 1 1
  • D6
  • E11

Q9:

Assume that l i m 𝑓 ( 𝑥 ) = 5 , l i m 𝑔 ( 𝑥 ) = 8 , and l i m ( 𝑥 ) = 9 . Find l i m ( 𝑓 ( 𝑥 ) 𝑔 ( 𝑥 ) ( 𝑥 ) ) .

Q10:

Given that l i m 𝑓 ( 𝑥 ) 4 𝑥 = 4 , determine l i m 𝑓 ( 𝑥 ) 𝑥 .

Q11:

Consider the graph of 𝑓 ( 𝑥 ) .

Find l i m ( 2 𝑥 𝑓 ( 𝑥 ) ) .

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