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ookt2c
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a challenge problem in my book states why dosent lhopitals rule work on the limit as x goes to infinity of (x^2+sinx)/x^2. I am stumped
ookt2c said:a challenge problem in my book states why dosent lhopitals rule work on the limit as x goes to infinity of (x^2+sinx)/x^2. I am stumped
ookt2c said:a challenge problem in my book states why dosent lhopitals rule work on the limit as x goes to infinity of (x^2+sinx)/x^2. I am stumped
arildno said:No, slider.
One of the conditions for the applicability of Hospital's rule is that the limit of the fraction of the derivatives MUST exist.
In this case, that limit does not exist, but the limit of our original expression exist NONETHELESS (equaling 1).
Read John's link carefully.
Which limit? The limit of the original problem certainly exists but arildno's point is that trying to apply L'Hopital's rule the derivative of the numerator is 2x+ cos(x) and that has no limit as x goes to infinity.John Creighto said:If you apply it once the limit still exists.
HallsofIvy said:Which limit? The limit of the original problem certainly exists but arildno's point is that trying to apply L'Hopital's rule the derivative of the numerator is 2x+ cos(x) and that has no limit as x goes to infinity.
arildno said:No, slider.
One of the conditions for the applicability of Hospital's rule is that the limit of the fraction of the derivatives MUST exist.
In this case, that limit does not exist, but the limit of our original expression exist NONETHELESS (equaling 1).
Read John's link carefully.
L'Hopital's Rule is a mathematical technique used to evaluate limits of indeterminate forms, such as 0/0 or ∞/∞. It states that if the limit of the ratio of two functions is indeterminate, then the limit of the ratio of their derivatives will be the same.
There are a few possible reasons why L'Hopital's Rule may not be working for a specific limit. One common reason is that the limit may not be in an indeterminate form, and therefore L'Hopital's Rule does not apply. Another reason could be that the derivatives of the functions involved do not exist at the point where the limit is being evaluated.
Yes, there are other methods for solving limits besides L'Hopital's Rule. Some common techniques include substitution, factoring, and using trigonometric identities. It may also be helpful to graph the functions involved to gain a better understanding of the limit.
One example is the limit as x approaches 0 of (x^2+sinx)/x^2. In this case, applying L'Hopital's Rule would result in a limit of 1, but the actual limit is 2. This is because the limit is not in an indeterminate form, and the derivatives of the numerator and denominator do not exist at x=0.
No, L'Hopital's Rule is not always a reliable method for solving limits. It should only be used when the limit is in an indeterminate form and the derivatives of the functions involved exist at the point where the limit is being evaluated. It is always important to double check the result obtained using L'Hopital's Rule to ensure its accuracy.