Three Tricky Limit Problems with Trig Functions

TLDRThis video discusses three tricky limit problems involving trig functions. The first problem involves the limit of sine(x)/(3x + tangent(x)) as x approaches 0, which simplifies to 1/4. The second problem deals with the limit of tangent(x)/(x^2 - 4) as x approaches 2, which also evaluates to 1/4. The third problem requires the use of a trig identity to rewrite the expression and find the limit of 2cos(x) - sin^2(x) as x approaches 0, which simplifies to 2.

Key insights

🔍Limit of sine(x)/(3x + tangent(x)) as x approaches 0 is 1/4.

📚Limit of tangent(x)/(x^2 - 4) as x approaches 2 is 1/4.

🍃By using a trig identity, we can rewrite 2cos(x) - sin^2(x) as 2.

Q&A

What is the limit of sine(x)/(3x + tangent(x)) as x approaches 0?

—The limit of sine(x)/(3x + tangent(x)) as x approaches 0 is 1/4.

What is the limit of tangent(x)/(x^2 - 4) as x approaches 2?

—The limit of tangent(x)/(x^2 - 4) as x approaches 2 is 1/4.

How can we rewrite 2cos(x) - sin^2(x)?

—By using a trig identity, we can rewrite 2cos(x) - sin^2(x) as 2.

Timestamped Summary

00:01Introduction to three tricky limit problems with trig functions.

01:40Explanation of the first problem involving the limit of sine(x)/(3x + tangent(x)) as x approaches 0.

04:40Solution to the first problem and evaluation of the limit as 1/4.

06:41Introduction to the second problem involving the limit of tangent(x)/(x^2 - 4) as x approaches 2.

09:57Solution to the second problem and evaluation of the limit as 1/4.

10:32Introduction to the third problem requiring the use of a trig identity.

14:54Solution to the third problem and evaluation of the limit as 2.

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