Trigonometric Limit Problem: Finding the Limit as x Approaches 0

Thread starter PotentialE
Start date Aug 25, 2012
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Limit Trigonometric

In summary, a trigonometric limit problem is a mathematical problem that involves finding the value of a trigonometric function at a specific point or as a variable approaches a certain value using calculus techniques. To solve these problems, one must identify the trigonometric function involved, use techniques such as algebraic manipulation and trigonometric identities, and consider special cases such as indeterminate forms. Trigonometric limit problems have various real-world applications in fields such as physics, engineering, and astronomy.

Aug 25, 2012

PotentialE

Homework Statement

find the limit as x approaches 0 of 3sin4x / sin3x

Homework Equations

sin2x = 2sinxcosx
lim as x ->0 of sinx / x =1

The Attempt at a Solution

sin4x = 2 sin2x cos2x

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Aug 25, 2012

kushan

Divide and multiply both numerator and denominator with the angles of resective sin .
You will get one famous limit , after that its a breeze

1. What is a trigonometric limit problem?

A trigonometric limit problem is a type of mathematical problem that involves finding the value of a trigonometric function at a specific point or as a variable approaches a certain value. It typically involves using concepts from calculus, such as limits and derivatives, to solve.

2. How do you solve a trigonometric limit problem?

To solve a trigonometric limit problem, you first need to identify which trigonometric function is involved and the specific point or value that the problem is asking for. Then, you can use various techniques such as algebraic manipulation, trigonometric identities, and the squeeze theorem to simplify the expression and evaluate the limit.

3. What are some common trigonometric identities used in solving limit problems?

Some common trigonometric identities used in solving limit problems include the Pythagorean identities, double-angle identities, and sum and difference identities. These identities can be used to simplify trigonometric expressions and make them easier to evaluate.

4. Are there any special cases to consider when solving trigonometric limit problems?

Yes, there are a few special cases to consider when solving trigonometric limit problems. These include limits involving trigonometric functions with vertical asymptotes, limits at infinity, and limits that involve indeterminate forms such as 0/0 or ∞/∞. In these cases, additional techniques such as L'Hopital's rule may be necessary.

5. What are some real-world applications of trigonometric limit problems?

Trigonometric limit problems have many real-world applications, especially in fields such as physics, engineering, and astronomy. For example, they can be used to determine the maximum height a projectile can reach, the velocity of a moving object, or the position of a planet in its orbit. They also play a crucial role in understanding and analyzing various wave phenomena, such as sound and light waves.