evaluate the limit of (sin(3+x)^2 - sin9) / x
as x approaches zero
You do know that the is a considerable number of mathematicians in the calculus reform movement who think that l’Hospital’s rule should be dropped “freshman” calculus. I remember the horror I felt upon hearing that proposed while attending a conference on ‘calculus instruction’ in 1988. In the years since I have come to embrace that point. This very thread proves the correctness of the point.
That is exactly what Plato did. He used the definition of the derivative.
So use,
Use and .
Mathstud28 is obsessed with L'hopitals for now. When you study it , you will be too
It has an irresistible charm of killing of limit problems instantaneously.
I agreeOriginally Posted by Mathstud28
But when you do so, also tell the alternative cool method to the poster. After all thats what they have to write in the exam
Isomorphism showed you
Apply the knowledge gained from this example
Direct substitution yields
YOu have two routes...L'hopital's or this method
THe definition of a derivative evaluated at a point c is
Now this looks an awful lot like that...since arctan(0)=0
This can be rewritten as
which is exactly like that formula I just showed you
so we have the right side of the formul all we need is the left side
So in this case it would be
and since
we know that
so
thus the limit is one
Hello,
Because the text states to use the definition of the derivative ?
Plus, it's really boring to always see that you do the apology of this rule... If someone is asked to do a way, then he has to do this way if it is that clear... doesn't he ?
So why do you bother if you don't explain ?You are right..that is a better method but more difficult to explain
Using the chain rule :