- #1
Moose352
- 166
- 0
Why can't I solve this?
[tex]
\lim_{x\rightarrow 0} \frac{\sqrt{1+\tan(x)}-\sqrt{1+\sin(x)}}{x^3}
[/tex]
[tex]
\lim_{x\rightarrow 0} \frac{\sqrt{1+\tan(x)}-\sqrt{1+\sin(x)}}{x^3}
[/tex]
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Moose352 said:No I'm not familiar with L'Hopital's rule. I looked it up in my book (it was listed as L'Hospital's rule ) but I'm quite sure the problem should be able to be solved without using L'Hopital's rule.
HallsofIvy said:To Moose353: Sorry, I didn't see the 1+ cos(x) in the denominator. I see nothing wrong with your solution.
To Loseyourname: Hello3719's point is that drawing a graph and observing that it APPEARS to converge to 1/4 doesn't prove that it does (as opposed to converging to 0.2500000000000000000000000000001, say).
L'Hopital's rule is a mathematical concept that is used to evaluate limits of indeterminate forms. In the context of graph problems, it is used to find the limit of a function at a specific point on the graph.
L'Hopital's rule should be used when a limit of a function at a specific point on the graph gives an indeterminate form, such as 0/0 or ∞/∞. It can also be used when trying to evaluate the limit of a quotient of two functions that are both approaching 0 or ∞.
Yes, there are limitations to using L'Hopital's rule in graph problems. It can only be used when dealing with functions that are continuous and differentiable at the point in question. Additionally, it can only be used when the limit is approaching a finite number or ∞.
No, L'Hopital's rule is only applicable to certain types of graph problems, specifically those involving limits and indeterminate forms. It cannot be used to solve other types of graph problems, such as finding the minimum or maximum of a function.
Yes, there are alternative methods to solving graph problems without using L'Hopital's rule. These include using algebraic manipulation, substitution, and graphing techniques. However, L'Hopital's rule is often the most efficient and accurate method for solving certain types of graph problems.