Worksheet: Limits of a Difference of Powers

In this worksheet, we will practice evaluating limits of a difference of powers.

Q1:

Determine lim𝑥4.

  • A1128
  • B1320
  • C5256
  • D5128
  • EThe limit does not exist.

Q2:

Find lim𝑥5𝑥6𝑥+1+𝑥+1𝑥+1.

  • A143
  • BThe limit does not exist.
  • C173
  • D223
  • E8

Q3:

Find lim2𝑥16+44𝑥16𝑥12𝑥164.

  • A4
  • B132
  • C116
  • D0
  • EThe limit does not exist.

Q4:

Discuss the existence of lim𝑓(𝑥) given 𝑓(𝑥)=𝑥+512𝑥+1286<𝑥<0,8𝑥2𝑥8𝑥6𝑥0<𝑥<𝜋2.ifcossinif

  • AThe limit does not exist.
  • B4
  • C367
  • D736
  • E97

Q5:

Find lim𝑓(𝑥) given 𝑓(𝑥)=𝑥+1𝑥+14<𝑥<0,7𝑥2𝑥9𝑥2𝑥0<𝑥<𝜋2.ifcossinif

  • A7𝜋18𝜋2
  • B𝜋18𝜋12
  • C7𝜋9𝜋6
  • D7𝜋18𝜋12
  • Edoes not exist

Q6:

Find lim𝑓(𝑥) given 𝑓(𝑥)=𝑥+1𝑥+18<𝑥<0,4𝑥2𝑥9𝑥5𝑥0<𝑥<𝜋2.ifcossinif

Q7:

Find lim𝑥+1𝑥+1𝑥.

  • A1342
  • B142
  • C1342
  • D142
  • Ehas no limit

Q8:

Find lim𝑥+𝑥2𝑥1.

Q9:

Find lim5𝑥419𝑥81.

  • A0
  • B57
  • C257
  • D563
  • E2563

Q10:

Find lim(3𝑥4)+2𝑥20𝑥2.

Q11:

Find lim𝑥1(𝑥1)×1𝑥1.

  • A281
  • BThe limit does not exist.
  • C427
  • D12881

Q12:

Find lim𝑥8𝑥512.

  • A164
  • B0
  • C1192
  • D13

Q13:

Given that limlim𝑥+8𝑥+2=𝑥𝑘𝑥𝑘, determine all the possible values of 𝑘.

  • A𝑘=6
  • B𝑘=8
  • C𝑘=3,𝑘=3
  • D𝑘=6,𝑘=6
  • E𝑘=1,𝑘=1

Q14:

Find lim(𝑥+1)1𝑥+2166.

Q15:

Find lim𝑥+𝑥2𝑥1.

  • A1132
  • B733
  • C433
  • DThe limit doesn’t exist.
  • E128

Q16:

Find lim36𝑥16𝑥1.

Q17:

Find lim𝑥𝑥𝑥𝑥.

  • A718
  • BThe limit does not exist.
  • C176
  • D617
  • E819

Q18:

Find lim𝑥625𝑥125.

  • Ahas no limit
  • B203
  • C5
  • D20
  • E154

Q19:

Find lim(𝑥4)+8𝑥2.

Q20:

Find lim𝑥243𝑥2,187.

  • A563
  • B745
  • C563
  • D19
  • EThe limit does not exist.

Q21:

Find lim𝑥481𝑥7.

Q22:

Find lim𝑥+102𝑥6.

  • A132
  • BThe limit does not exist.
  • C132
  • D16
  • E12

Q23:

If lim𝑥81𝑥27=𝑙, what are the values of 𝑛 and 𝑙?

  • A𝑛=4, 𝑙=13
  • B𝑛=3, 𝑙=13
  • C𝑛=3, 𝑙=49
  • D𝑛=4, 𝑙=4

Q24:

Determine the value of lim𝑥2𝑥2 to the nearest hundredth.

Q25:

Given that 𝑓(𝑥)=1𝑥, find lim𝑓(𝑥)𝑓(2)𝑥4.

  • A643
  • B364
  • CThe limit does not exist.
  • D364
  • E643

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