Worksheet: Indeterminate Forms and L'Hôpital's Rule

In this worksheet, we will practice applying L’Hôpital's rule to evaluate the limits of the indeterminate forms 0.∞, 0^∞, 1^∞, 0^0, and ∞ - ∞.

Q1:

Use l’HΓ΄pital's rule to determine the limit of π‘›οŽ ο‘ƒ as π‘›β†’βˆž.

Q2:

Given that limο—β†’βˆžπ‘₯=∞ and limο—β†’βˆžοŠ±ο—π‘’=0,by writing π‘₯π‘’οŠ±ο— as π‘₯𝑒, use l’HΓ΄pital's rule to determine limο—β†’βˆžοŠ±ο—π‘₯𝑒.

Q3:

Use l’HΓ΄pital's rule to determine limο—β†’βˆžπ‘₯.οŽ ο‘

Q4:

Use l’HΓ΄pital's rule to determine limsinο—β†’οŠ¦ο€Ό1π‘₯βˆ’1π‘₯.

Q5:

Find limlnο—β†’οŠ¦οŽ©ο€Ό5π‘₯βˆ’83π‘₯.

  • A0
  • B ∞
  • C βˆ’ 8 3
  • D βˆ’ ∞

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