Worksheet: Limits at Infinity and Unbounded Limits

In this worksheet, we will practice evaluating limits of a function when x tends to infinity and exploring unbounded limits that tend to infinity as x approaches a certain value.

Q1:

Find lim6𝑥𝑥6.

  • A1
  • B
  • C6
  • D0

Q2:

Find lim16𝑥+89𝑥+3.

  • A
  • B43
  • C169
  • D0

Q3:

Find lim𝑥+38𝑥+9𝑥+1.

  • A
  • B18
  • C3
  • D0

Q4:

Find lim3𝑥8𝑥+47𝑥(2𝑥+7).

  • A118
  • B
  • C45196
  • D0

Q5:

Find lim3𝑥4𝑥+8.

  • A0
  • B38
  • C
  • D34

Q6:

Find lim3𝑥𝑥𝑥+3𝑥+2𝑥8𝑥𝑥5𝑥8.

  • A
  • B
  • C3
  • D3

Q7:

Find lim98𝑥+6𝑥2𝑥.

  • A5
  • B9
  • C
  • D
  • E2

Q8:

Consider the polynomial 𝑓(𝑥)=5𝑥+9𝑥2𝑥𝑥+11.

Which of the following is equal to lim𝑓(𝑥)?

  • A𝑥lim
  • Blim11
  • C2𝑥lim
  • D5𝑥lim

Hence, find lim𝑓(𝑥).

  • A2
  • B
  • C5
  • D11
  • E

Q9:

Find lim7𝑥+8𝑥+45𝑥+3𝑥.

Q10:

Consider the rational function 𝑓(𝑥)=3𝑥8𝑥92𝑥.

Which of the following is equal to lim𝑓(𝑥)?

  • A3891𝑥+2lim
  • B381𝑥91𝑥2limlim
  • C3+81𝑥91𝑥+2limlim
  • D381𝑥92lim
  • E3891𝑥2lim

Find lim𝑓(𝑥).

  • A57
  • B52
  • C52
  • D32
  • E32

Q11:

Find lim2𝑥+8𝑥𝑥+9𝑥42𝑥6𝑥+7𝑥+6𝑥+3.

  • A
  • B43
  • C43
  • D

Q12:

Determine lim(5𝑥+4)(2𝑥+4)(𝑥+2)(5𝑥+1).

  • A0
  • B85
  • C
  • D2
  • E

Q13:

Determine lim5𝑥+3(𝑥5)(4𝑥3𝑥), if it exists.

  • A254
  • B54
  • C0
  • DThe limit does not exist.
  • E25

Q14:

Find lim𝑥36𝑥+3𝑥+33𝑥.

  • A0
  • B3
  • C
  • D

Q15:

Determine lim64𝑥+3𝑥+44𝑥+2𝑥.

  • A
  • B110
  • C

Q16:

Find lim𝑛𝑎+1𝑛𝑎.

  • A𝑎
  • B5𝑎
  • C5𝑎
  • D4𝑎

Q17:

Find the values of 𝑎 and 𝑏, given that lim𝑓(𝑥)=4 and lim𝑓(𝑥)=5, where 𝑓(𝑥)=𝑎𝑥54𝑏𝑥𝑥+4.

  • A𝑎=18, 𝑏=2
  • B𝑎=16, 𝑏=16
  • C𝑎=16, 𝑏=2
  • D𝑎=4, 𝑏=2
  • E𝑎=4, 𝑏=16

Q18:

Determine lim2𝑥𝑥9𝑥+2(2𝑥+5).

  • A
  • B
  • C14
  • D1

Q19:

Determine lim8𝑥+76|𝑥|2.

  • A43
  • B72
  • C0
  • D
  • E

Q20:

Find lim4𝑥36𝑥+3+8𝑥7𝑥+39𝑥+5𝑥+5.

  • A
  • B
  • C89
  • D149
  • E23

Q21:

If 𝑓(𝑥) is a polynomial function of a fifth degrees, and 𝑔(𝑥) is a polynomial function of a fourth degrees, find lim𝑔(𝑥)4𝑥𝑓(𝑥).

  • A±
  • Breal number0
  • Chas no limit
  • Dzero

Q22:

Find lim3𝑥5𝑥3+26.

  • A5
  • B135
  • C2
  • D35

Q23:

Find the values of 𝑎 and 𝑏, given that lim5𝑥2𝑥+3(𝑎+4)𝑥+(1𝑏)𝑥+5𝑥=.

  • A𝑎=4, 𝑏=1
  • B𝑎=4, 𝑏=1
  • C𝑎=4, 𝑏=1
  • D𝑎=4, 𝑏=1

Q24:

By rationalizing and using limit laws, determine lim𝑛+3𝑛𝑛.

  • A3
  • B2
  • C6
  • D32
  • E12

Q25:

Find lim4𝑥+5𝑥+8.

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