The limit Lim (√x - √a)/(x - a) as x approaches a can be evaluated using two methods: L'Hôpital's rule and rationalization of the numerator. L'Hôpital's rule applies due to the zero-over-zero indeterminate form, allowing the derivatives of the numerator and denominator to be taken. Alternatively, rationalizing the numerator simplifies the expression without the need for derivatives, leading to a clearer solution.
PREREQUISITESStudents studying calculus, particularly those tackling limits and derivatives, as well as educators looking for effective teaching methods for these concepts.
You might consider rationalizing numerator. Then there's no need to use L'Hôpital's rule.TyChi said:Homework Statement
Evaluate the limit
Lim (√x-√a)/(x-a)
x→a
I am not sure how to solve this. I asked my classmates and they do not know either. Help would be much appreciated!