If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.PeroK said:What exactly is the problem?
Why not?heythere1010 said:If I sub in 4 from the beginning, I will get sqrt 0. I can't have that as my answer.
I thought you would need to do something like conjugates for it.PeroK said:Why not?
The limit x→4 √x-4 approaches 0, as the x-value gets closer and closer to 4.
Rationalizing the limit helps to simplify the expression and make it easier to evaluate the limit. It also allows us to find the exact value of the limit, rather than just an approximation.
To rationalize the limit x→4 √x-4, we can multiply the expression by its conjugate, which is √x+4. This will eliminate the radical in the numerator and allow us to evaluate the limit.
No, the limit x→4 √x-4 only applies to functions that have a rational or irrational exponent. It cannot be used for functions with a logarithmic or trigonometric exponent.
Yes, if the limit x→4 √x-4 is in the form of a rational function, we can use L'Hôpital's rule to evaluate it. This rule states that if the limit of the numerator and denominator both approach 0 or infinity, we can take the derivative of both and evaluate the new limit.