Worksheet: Limits by Direct Substitution

In this worksheet, we will practice using the direct substitution method to evaluate limits.

Q1:

Determine lim(9𝑥6𝑥9).

Q2:

Determine lim4𝑥9𝑥+1.

  • A 2 6 1
  • B244
  • C 9 3
  • D 1 1 2

Q3:

Find lim(30).

Q4:

Determine limsin9𝑥5𝑥.

  • A 1 8 2 5 𝜋
  • B 3 6 5 𝜋
  • C 1 8 2 𝜋
  • D 9 2 1 0 𝜋
  • E 2 2 5 𝜋

Q5:

Given 𝑓(𝑥)=|𝑥+11||𝑥18|, find lim𝑓(𝑥).

Q6:

Find an exact expression for lim𝑥𝑥+2𝑥+7𝑥+1 using the limit laws.

  • A 1 5 5
  • B 5 9 5 5
  • C 8 3 5 5
  • D 6 7 5 5
  • E 5 5

Q7:

Find lim7𝑥+73𝑥3.

  • A 7 3
  • B 3
  • C 2 1 8
  • D 8

Q8:

Find limsin(48𝑥).

  • A0
  • B8
  • C4
  • D 8

Q9:

Find limcos𝑥(24𝑥)𝑥+𝑥.

  • A 2 3
  • B 1 3
  • C 1 2
  • D0

Q10:

Find limtansincos73(3𝑥)7(5𝑥)+5(6𝑥).

  • A0
  • B7
  • C 9 6 5
  • D 7 5
  • E 3 1 1

Q11:

Find lim𝑥+10𝑥11𝑥+11𝑥.

  • A 1 1 0 1 1
  • B11
  • C 5 5 1 1
  • D 1 1
  • E 1 0 1 1

Q12:

Find lim1(𝑥5).

  • A0
  • B 1
  • CThe limit does not exist.
  • D 5

Q13:

If the function 𝑓(𝑥)=|𝑥+9||𝑥12|, find lim𝑓(𝑥).

Q14:

If the function 𝑓(𝑥)=|𝑥+1||𝑥5|, find lim𝑓(𝑥).

Q15:

Determine lim𝑥9𝑥+28𝑥3𝑥9.

  • A 5 4 1 2 5
  • B 1 4 9
  • C50
  • D 5 4 1 2 5
  • EThe limit does not exist.

Q16:

Determine limcos7𝑥𝑥.

  • A 7 𝜋 6
  • B 7 𝜋 3
  • C3
  • D 𝜋 6

Q17:

Find limtansincos15𝑥5𝑥5𝑥.

Q18:

Find limcos63𝑥5𝑥.

Q19:

Determine lim𝑥.

  • A 1 7
  • B 5 1 4
  • C 1 1 4
  • D 1 2

Q20:

Given that lim𝑎𝑥1=6, what is 𝑎?

  • A 2 9 5
  • B 3 6
  • C 1
  • D 2 0

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