can't we apply L'hopital's rule for all the limits questions ?
I know that it can be used only if it is an undetermined foam.But if it is a determined form,will there be a question to find the limit of?we can easily figure it out
The perfect example is .
The reason being because to use L'Hospital's Rule, you need to evaluate the derivatives of the numerator and the denominator, but evaluating the derivative of involves evaluating - the exact same limit!
Notice that you have to evaluate , which is the EXACT same limit as . How could you possibly argue that using L'Hospital's Rule is appropriate in this case, because evaluating the derivative of implies you have already found the very limit you are trying to find? It's entirely circular reasoning.
Here's a trivial example.
Both numerator and denominator, separately go to 0 but it you try to use L'Hopitals rule you just keep getting
so that L'Hopital's rule does not work.
Of course, the limit is 1.
Here's another one (although not as trivial as Halls ex.) that sends you in a circular pattern
Point is - when L'Hopital's method doesn't work, sometimes you have to be more creative.