Worksheet: Evaluating Limits Using Algebraic Techniques

In this worksheet, we will practice using algebraic techniques like factorization to evaluate limits.

Q1:

Find lim3𝑥18𝑥+24𝑥16.

  • A 3 4
  • B0
  • C4
  • D 3 2
  • E 9 4

Q2:

Determine lim𝑥32𝑥2.

Q3:

Find lim𝑥2𝑥2𝑥6𝑥+4.

  • A1
  • B 1
  • C2
  • D0
  • E 1 3

Q4:

Find lim𝑥256𝑥16.

  • A32
  • BThe limit does not exist.
  • C 1 8
  • D8

Q5:

Find lim8𝑥64𝑥4.

  • A32
  • B8
  • C2
  • D0
  • E24

Q6:

Find lim(𝑥4)16𝑥.

Q7:

Find lim𝑥44𝑥8.

Q8:

Find lim(𝑥6)𝑥+2𝑥+1𝑥6𝑥7.

Q9:

Find lim9𝑥127𝑥1.

  • A 2 3
  • B2
  • CThe limit doesn’t exist.
  • D 3 2

Q10:

Find lim6𝑥486𝑥+(𝑥8)48.

Q11:

Find lim𝑥9𝑥+3.

Q12:

Find lim25𝑥35𝑥125𝑥+3.

Q13:

Find lim𝑥+642𝑥+6𝑥8.

  • A0
  • B 2 4 5
  • C 8 5
  • D48

Q14:

Find lim𝑥36𝑥+216.

  • A 9
  • B 2 3
  • C 1 9
  • DThe limit does not exist.
  • E 3 2

Q15:

Find lim6𝑥+53𝑥+43𝑥+243𝑥+22𝑥16.

  • A 3 4 7 8
  • B347
  • CThe limit does not exist.
  • D 3 4 7 2 6
  • E 3 4 7 2 6

Q16:

Find lim𝑥+13𝑥+40𝑥+9𝑥12𝑥160.

  • AThe limit doesn’t exist.
  • B1
  • C 8 3
  • D 1 1 2
  • E 1 3

Q17:

Find lim4𝑥+2𝑥13𝑥+7𝑥𝑥.

  • A3
  • B 3 2
  • C 3 2
  • DThe limit does not exist.

Q18:

Find lim𝑥81𝑥27.

  • A 9 4
  • BThe limit does not exist.
  • C4
  • D1
  • E 3

Q19:

Find lim𝑥2𝑥8.

  • A 1 1 6
  • B 1 4
  • C 1 1 2
  • DThe limit does not exist.
  • E 1 8

Q20:

Find lim𝑥23𝑥2𝑥4.

  • A 2
  • B 1 5
  • C 2 5
  • D 1

Q21:

Find lim9𝑥+5𝑥143𝑥7𝑥+4.

  • A 3 2 5
  • B 5 7
  • C3
  • D 7 2

Q22:

Find lim𝑥+18𝑥19𝑥𝑥.

  • A20
  • B19
  • C 2 5
  • D 3 2

Q23:

Find lim𝑥25𝑥+23𝑥12.

  • A 1 1 0 2
  • B 1 9 2
  • C 1 1 3 8
  • D 1 6 8

Q24:

Find lim𝑥𝑥4+𝑥6𝑥4.

  • A0
  • B 5 4
  • C 1 4
  • D 6

Q25:

Find lim2𝑥+11𝑥+143𝑥+11𝑥+10.

  • A 2
  • B 3 1 1
  • C0
  • D11
  • E 3

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