Limits with sinx where x tends to infinity help.

In summary, the conversation discusses a problem with solving a limit using L'Hopital's rule and the difficulty of finding the correct answer. It is suggested to try solving another limit to help solve this one.
  • #1
quackdesk
7
0

Homework Statement


http://prikachi.com/images/26/4273026B.gif


Homework Equations




The Attempt at a Solution


I'm having problems in solving the limit which is shown on the gif file .
As you see I use L'Hopital's rule 2 times and I get to a point when I should divide -sinx with sinx which results in -1 instead of 1 which is the right answer according to the key.

P.S sorry for posting the same thread in another sub-forum before I came here.
 
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  • #2
quackdesk said:

Homework Statement


http://prikachi.com/images/26/4273026B.gif


Homework Equations




The Attempt at a Solution


I'm having problems in solving the limit which is shown on the gif file .
As you see I use L'Hopital's rule 2 times and I get to a point when I should divide -sinx with sinx which results in -1 instead of 1 which is the right answer according to the key.

P.S sorry for posting the same thread in another sub-forum before I came here.

You should have stopped after the first differentiation. (1+cos(x))/(1-cos(x)) doesn't have indeterminant form. You can't apply l'Hopital again. And the limit of that expression as x->infinity doesn't exist. So l'Hopital doesn't apply. You'll have to think of another way to find the limit or show one doesn't exist.
 
  • #3
Solving this limit may help (you can even use l'Hopital's rule!)
lim x->infinity sinx/x
 

FAQ: Limits with sinx where x tends to infinity help.

What is the limit of sinx as x approaches infinity?

The limit of sinx as x approaches infinity does not exist. As x gets larger and larger, the values of sinx will oscillate between -1 and 1, never approaching a specific value.

How can I evaluate limits with sinx as x approaches infinity?

To evaluate limits with sinx as x approaches infinity, you can use the Squeeze Theorem, which states that if two functions have the same limit at a point, then any function squeezed between them will also have the same limit at that point.

Can I use L'Hopital's Rule to evaluate limits with sinx as x approaches infinity?

No, L'Hopital's Rule cannot be applied to limits with sinx as x approaches infinity since the limit does not exist. L'Hopital's Rule only applies to limits that approach a specific value.

How can I graph limits with sinx as x approaches infinity?

To graph limits with sinx as x approaches infinity, you can use a graphing calculator or software to plot the values of sinx as x gets larger. The resulting graph will show the oscillating behavior and the lack of a specific limit.

Are there any real-world applications for limits with sinx as x approaches infinity?

Yes, limits with sinx as x approaches infinity can be used in physics and engineering to model oscillating systems, such as pendulums and springs. They can also be used in signal processing to analyze signals that have a sinusoidal component.

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