# L'Hôpital's Rule

See how to solve the limit by using the L'Hôpital's rule.

2 examples and their solutions.

## L'Hôpital's Rule

### Rule

limx → af(x)g(x) = limx → af'(x)g'(x)

Use this formula to solve 0/0 form limit. ### Example

limx → 0sin 4xx

Solution limx → 0sin 4xx

= limx → 0(cos 4x)⋅41 - [1] [2]

= (cos 0)⋅41

= 1⋅41 - [3]

= 4

= limx → 0(cos 4x)⋅41 - [1] [2]

= (cos 0)⋅41

= 1⋅41 - [3]

= 4

Close

### Example

limx → 0e

Solution ^{x}- 12x limx → 0e

= limx → 0e

= limx → 0e

= e

= 12 - [3]

^{x}- 12x= limx → 0e

^{x}- 02 - [1] [2]= limx → 0e

^{x}2= e

^{0}2= 12 - [3]

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