Limits & L'Hôpital's Rule Help

Need Help with Limits and L'Hôpital's Rule

Welcome to the calculus forum! Discuss and find solutions to problems involving limits and the application of L'Hôpital's Rule.

User123

January 5, 2034, 10:15 AM

I'm stuck on a problem where I need to evaluate lim (x -> 0) [(sin(x))/x]. I think L'Hôpital's Rule might help, but I'm not sure how to apply it.

MathGuru007

January 5, 2034, 11:45 AM

Hi User123! You’re on the right track with L'Hôpital’s Rule. Given that (sin(x))/x becomes 0/0 as x approaches 0, you can differentiate the numerator and the denominator separately. In this case, the derivative of sin(x) is cos(x), and the derivative of x is 1. Thus, lim (x -> 0) [cos(x)/1] = 1. 😊