What is the result of this limit and why?

[itsrayex]

I tried to solve it in 3 different ways but could not. Could you please help me? I gave up on the second method and Hopital cause I saw it wasnt getting me anywhere

 

[Deleted member 4993]

View attachment 31036
I tried to solve it in 3 different ways but could not. Could you please help me? I gave up on the second method and Hopital cause I saw it wasnt getting me anywhere
View attachment 31037

For L'Hopital

The numerator .........................d/dx [log(1 -5x)] = -5/(1- 5x)

The denominator .........................d/dx (1 - e^2x) = - 2 * e^2x

continue.......

 

[BigBeachBanana]

Seem like you’re mixing up l’hopital and quotient rule.