Limit of a trigonometric function without l'hopitals rule?

In summary, the limit of a trigonometric function is the value that the function approaches as the input approaches a certain value. It can be found by graphing the function or using trigonometric identities to simplify the expression. Some common identities that can be useful are the Pythagorean, reciprocal, and double angle identities. The limit of a trigonometric function can be undefined if there is a vertical asymptote at the desired input value. Special cases for finding the limit include when the input approaches 0 or infinity, in which case rewriting the function or using identities may be helpful.
  • #1
stony
4
0

Homework Statement



lim of (sin(x)/(x+sin(x)) as x approaches 0

Homework Equations


none


The Attempt at a Solution


I tried using trigonometric identites to figure it out but I can't do it, and when I looked up help for it I only found solutions that utilize the l'hopitals rule. I have to know how to do these questions without this rule, can someone at least get me started in the right direction please? Thanks.
 
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  • #3
Try dividing the top and bottom by x.
 

FAQ: Limit of a trigonometric function without l'hopitals rule?

What is the definition of the limit of a trigonometric function?

The limit of a trigonometric function is the value that the function approaches as the input approaches a certain value. It can also be thought of as the y-value of the function at a specific x-value.

How can I find the limit of a trigonometric function without using L'Hopital's rule?

One method is to graph the function and observe the behavior as the input approaches the desired value. Another method is to use trigonometric identities to simplify the function and then evaluate the limit.

What are some common trigonometric identities that can be useful in finding limits?

Some common identities include the Pythagorean identities, reciprocal identities, and double angle identities. These can be used to simplify trigonometric expressions and make it easier to evaluate limits.

Can the limit of a trigonometric function be undefined?

Yes, the limit of a trigonometric function can be undefined if the function has a vertical asymptote at the desired input value. This means that the function approaches positive or negative infinity as the input approaches the specified value.

Are there any special cases when finding the limit of a trigonometric function?

Yes, special cases include when the input approaches 0 and when the input approaches infinity. In these cases, it may be helpful to use trigonometric identities or to rewrite the function in terms of another variable before evaluating the limit.

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