# How do to solve:Lim (tg 5x)/(4x) whit x-> 0Thanks!must be resolved based on the remarkable limits

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Expert Answers

sciencesolve | Certified Educator

Use the remarkable limit `lim_(u(x)->0)``(tan u(x))/u(x) = 1`

You should create this remarkable limit in your function, therefore you should divide and multiply by the argument of tangent function.

`lim_(x-gt0) ((tan 5x)/(5x))*(5x/4x) = lim_(x-gt0)((tan 5x)/(5x))*lim_(x-gt0)(5x)/(4x)`

`lim_(x-gt0)((tan 5x)/(4x))= 1*lim_(x-gt0)((5x)/(4x)) = 5/4`

**Therefore, the limit of the fraction`((tan 5x)/(4x))` is 5/4.**