L'Hopital's Rule

LHopital's Rule helps us to find the limit of an Undefined limits, like 0/0, ∞/∞ and such. It's quite simple to apply and very convenient to solve some problems.

Refer to L'Hôpital's rule

▶ Back previous note on: Asymptote of Rational Expressions ▶ Practice at Khan academy: Disguised derivatives

From my experience, the L'Hopital's Rule is so often been used that we didn't even realize. Actually it's been used almost every time when we are to evaluate the LIMITS OF RATIONAL EXPRESSIONS.

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Example of 0/0

Example of ∞/∞

1. Find the limit: Solve:

2. Find the limit: Solve:

Example of 1^∞

L'Hopital Rule for Composite functions

Example of composite exponential function

Solve:

• Direct plug in the x=2 and get limit = 1^∞, which is an indeterminate form

• So we're gonna apply the Log Power Rule to take down the power:

  

• We use Natural Log for doing this:

  

• And now we can apply the L'Hopital Rule for ln(y):

  

• From ln(y) we could get limit of y: