Need verification to solution for trig function limit question

In summary, the problem is finding the limit of (sin 4x) / (sin 6x) as x approaches 0. After using some algebra and Limit Laws, the final answer is 2/3. L'Hopital's rule can also be used to solve this problem.
  • #1
kylera
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As I do not have the solution book and classes are over for the summer, I don't have any other way of verifying whether this is right or not.

Homework Statement


lim(x->0) (sin 4x) / (sin 6x)


Homework Equations





The Attempt at a Solution


If I may temporarily remove the lim sign...
[tex]\frac{sin 4x}{sin 6x} = \frac{sin4x}{4x} \times \frac{4x}{sin6x}[/tex]

[tex] = \frac{sin4x}{4x} \times \frac{6x}{sin6x} \times \frac{4x}{6x}[/tex]

By Limit Laws, take the limit of each fraction to get
[tex]1 \times 1 \times \frac{4}{6}[/tex]

4. Final answer
2/3
 
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  • #2
You could also use L'Hopital rule to get the same result.
 
Last edited:

FAQ: Need verification to solution for trig function limit question

1. What is a limit in trigonometric functions?

A limit in trigonometric functions is the value that a function approaches as its input approaches a certain value. In other words, it is the value that the function "approaches" or gets closer and closer to, but may not actually reach, as the input gets closer and closer to a specific value.

2. How do I solve for a limit in a trigonometric function?

To solve for a limit in a trigonometric function, you can use algebraic techniques, trigonometric identities, or L'Hopital's rule. It is important to also consider any potential restrictions on the domain of the function.

3. What is the difference between a one-sided and two-sided limit in trigonometric functions?

A one-sided limit in trigonometric functions is when the function is approaching the limit from only one direction, either the left or right side. A two-sided limit is when the function is approaching the limit from both the left and right sides, and the values from both sides must be equal for the limit to exist.

4. How do I know if a limit in a trigonometric function exists?

A limit in a trigonometric function exists if the function approaches the same value from both the left and right sides, and that value is a real number. If the function approaches different values from the left and right sides, or if the function approaches infinity, the limit does not exist.

5. Can I use a calculator to solve for a limit in a trigonometric function?

In most cases, a calculator can be used to approximate the value of a limit in a trigonometric function, but it is important to remember that calculators are not always accurate and can only provide an approximation. It is recommended to also use algebraic techniques or trigonometric identities to verify the solution.

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