Worksheet: One-Sided Limits

In this worksheet, we will practice evaluating one-sided limits graphically and algebraically.

Q1:

Determine lim𝑓(𝑥).

Q2:

Find lim𝑓(𝑥), if it exists.

Q3:

Find lim𝑥+18𝑥+81𝑥7𝑥18.

  • A
  • B9
  • C0
  • D

Q4:

Determine lim𝑓(𝑥) and lim𝑓(𝑥), given that 𝑓(𝑥)=𝑥+9𝑥9,1𝑥+9𝑥>9.ifif

  • Alim𝑓(𝑥)does not exist,lim𝑓(𝑥)does not exist
  • Blim𝑓(𝑥)=0,lim𝑓(𝑥)does not exist
  • Clim𝑓(𝑥)=0,lim𝑓(𝑥)=19
  • Dlim𝑓(𝑥)=0,lim𝑓(𝑥)=0

Q5:

Find lim𝑓(𝑥) given 𝑓(𝑥)=7𝑥+3𝑥5𝑥𝜋2<𝑥<0,52𝑥+70<𝑥<𝜋2.sinsinifcosif

  • A2
  • B532+7
  • C92
  • D3+7𝜋3

Q6:

Find lim𝑓(𝑥) given 𝑓(𝑥)=5𝑥5𝑥+25𝑥𝑥0<𝑥<𝜋2,429𝑥+𝜋𝜋2<𝑥<𝜋.cossinifcosif

  • A4𝜋
  • B42+𝜋
  • C15
  • D42+𝜋

Q7:

Discuss the existence of lim𝑓(𝑥) given 𝑓(𝑥)=|𝑥1|+21<𝑥<2,𝑥+2𝑥8𝑥2𝑥2<𝑥<4.ifif

  • Alim𝑓(𝑥) does not exist because lim𝑓(𝑥) is undefined.
  • Blim𝑓(𝑥) exists and equals 5.
  • Clim𝑓(𝑥) exists and equals 2.
  • Dlim𝑓(𝑥) exists and equals 1.

Q8:

Given 𝑓(𝑥)=4𝑥44|𝑥11|, find 𝑓(11)+𝑓(11).

Q9:

Determine the following infinite limit: limlnsin5(𝑥).

  • A
  • B
  • C0
  • D5

Q10:

Determine the following infinite limit: limcot52𝑥.

  • A0
  • B
  • C5
  • D3𝜋
  • E

Q11:

Determine lim𝑓(𝑥) and lim𝑓(𝑥), given that 𝑓(𝑥)=𝑥+9𝑥7,1𝑥+9𝑥>7.ifif

  • Alim𝑓(𝑥)does not exist,lim𝑓(𝑥)does not exist
  • Blim𝑓(𝑥)=2,lim𝑓(𝑥)=12
  • Clim𝑓(𝑥)=2,lim𝑓(𝑥)does not exist
  • Dlim𝑓(𝑥)=2,lim𝑓(𝑥)=2

Q12:

Determine lim𝑓(𝑥), if it exists.

  • AThe limit does not exist.
  • B0
  • C6
  • D2

Q13:

Use the graph below to find lim𝑓(𝑥).

  • AThe limit does not exist.
  • B3
  • C4
  • D8

Q14:

Use the graph below to find lim𝑓(𝑥).

Q15:

Determine lim𝑓(𝑥), if it exists.

Q16:

Determine lim𝑓(𝑥), if it exists.

Q17:

Determine limlimlim𝑓(𝑥)+𝑓(𝑥)+𝑓(𝑥).

Q18:

Determine 𝑓(1).

Q19:

Determine lim𝑓(𝑥).

Q20:

Use the graph below to find lim𝑓(𝑥).

Q21:

Using the graph shown, find lim𝑓(𝑥).

Q22:

Determine lim𝑓(𝑥).

Q23:

Find lim𝑓(𝑥) and lim𝑓(𝑥), where 𝑓(𝑥)=78𝑥<9,9𝑥7𝑥9.ifif

  • Alimlim𝑓(𝑥)=74,𝑓(𝑥)=74
  • Blimlim𝑓(𝑥)=78,𝑓(𝑥)=78
  • Climlim𝑓(𝑥)=78,𝑓(𝑥)=74
  • Dlimlim𝑓(𝑥)=74,𝑓(𝑥)=78

Q24:

Determinelim𝑓(𝑥).

Q25:

Determine lim𝑓(𝑥).

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