Solving Trig Limit Question: Step-by-Step Guide

In summary, when solving a trigonometric limit question, it is important to recognize common trigonometric identities and apply them appropriately. The first step is to simplify the expression using algebraic manipulation or trigonometric identities. It is also important to determine if the question is indeterminate, which requires additional steps to solve. While a calculator may be helpful in checking work, it is important to show understanding of the concepts by solving by hand. One can check their solution by graphing the original function and simplified expression or plugging in values near the limit.
  • #1
Mejiera
15
0

Homework Statement



lim x appraoches 0 sin(x)/(x+tan(x))

Homework Equations



I have tryed everthing. Can someone show me how to do this.

The Attempt at a Solution

 
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  • #2
Have you tried L'Hopital's rule?
 
  • #3
Use L'Hopital's rule as Char suggested. The answer should come out to 1/2. If you have trouble applying the rule, let me know and i'll help you out.
 
  • #4
Another way to see this: squeeze theorem with sin(x)/2tan(x) and sin(x)/2x.
 

Related to Solving Trig Limit Question: Step-by-Step Guide

1. How do I know which trigonometric identity to use when solving a limit question?

The key to solving a trigonometric limit question is to recognize common trigonometric identities and apply them appropriately. This may involve converting trigonometric functions using identities such as sin^2x + cos^2x = 1 or using the double angle identities, among others. It is important to practice and become familiar with these identities in order to determine which one to use.

2. What is the first step in solving a trigonometric limit question?

The first step in solving a trigonometric limit question is to use algebraic manipulation or trigonometric identities to simplify the expression. This may involve factoring, expanding, or using identities to rewrite the expression in a more manageable form.

3. How do I determine if a trigonometric limit question is indeterminate?

A trigonometric limit question is indeterminate if it involves the ratio of two functions that both approach zero, or if it involves functions that approach infinity or negative infinity. These types of limit questions require additional steps to solve, such as using L'Hopital's rule or manipulating the expression to make it more manageable.

4. Can I use a calculator to solve a trigonometric limit question?

While a calculator may be helpful in checking your work, it is important to show your steps and understanding of the concepts when solving a trigonometric limit question. In most cases, you will not be allowed to use a calculator on a test or exam, so it is important to practice solving these questions by hand.

5. How can I check if my solution to a trigonometric limit question is correct?

You can check your solution by graphing the original function and your simplified expression on a graphing calculator. If the two graphs approach the same value as x approaches the given limit, then your solution is likely correct. You can also plug in a few values of x near the limit to see if your solution matches the output of the original function.

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