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.

  • A261
  • B244
  • C93
  • D112

Q3:

Find lim(30).

Q4:

Determine limsin9𝑥5𝑥.

  • A1825𝜋
  • B365𝜋
  • C182𝜋
  • D9210𝜋
  • E225𝜋

Q5:

Given 𝑓(𝑥)=|𝑥+11||𝑥18|, find lim𝑓(𝑥).

Q6:

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

  • A155
  • B5955
  • C8355
  • D6755
  • E55

Q7:

Find lim7𝑥+73𝑥3.

  • A73
  • B3
  • C218
  • D8

Q8:

Find limsin(48𝑥).

  • A0
  • B8
  • C4
  • D8

Q9:

Find limcos𝑥(24𝑥)𝑥+𝑥.

  • A23
  • B13
  • C12
  • D0

Q10:

Find limtansincos73(3𝑥)7(5𝑥)+5(6𝑥).

  • A0
  • B7
  • C965
  • D75
  • E311

Q11:

Find lim𝑥+10𝑥11𝑥+11𝑥.

  • A11011
  • B11
  • C5511
  • D11
  • E1011

Q12:

Find lim1(𝑥5).

  • A0
  • B1
  • CThe limit does not exist.
  • D5

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.

  • A54125
  • B149
  • C50
  • D54125
  • EThe limit does not exist.

Q16:

Determine limcos7𝑥𝑥.

  • A7𝜋6
  • B7𝜋3
  • C3
  • D𝜋6

Q17:

Find limtansincos15𝑥5𝑥5𝑥.

Q18:

Find limcos63𝑥5𝑥.

Q19:

Determine lim𝑥.

  • A17
  • B514
  • C114
  • D12

Q20:

Given that lim𝑎𝑥1=6, what is 𝑎?

Q21:

Which of the following functions does not satisfy the conditions for direct substitution of the limit lim𝑓(𝑥)?

  • A𝑓(𝑥)=32𝑥
  • B𝑓(𝑥)=𝑥23𝑥cos
  • C𝑓(𝑥)=𝑥𝑥2𝑥
  • D𝑓(𝑥)=𝑥2𝑥3
  • E𝑓(𝑥)=𝑥2𝑥+3

Q22:

Given that limcos2𝑎𝑥2𝑥=8, find the value of 𝑎.

Q23:

Given that lim𝑎𝑥5=5, find the value of 𝑎.

Q24:

Given that lim𝑎𝑥𝑥2=3, find the value of 𝑎.

Q25:

True or False: If the function 𝑓(𝑥) is a polynomial, then lim𝑓(𝑥)=𝑓(𝑎).

  • ATrue
  • BFalse

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