Limits and Trigonometric Identities

This video tutorial covers the topic of trigonometric limits, focusing on solving limit problems using various techniques such as substitution, factoring, and trigonometric identities. The instructor provides detailed explanations and step-by-step solutions to ten example problems, demonstrating how to handle limits approaching zero and other values. The video aims to enhance understanding of trigonometric limits and improve problem-solving skills.

What is the value of the limit as x approaches π/3 for sin(x)/cos(x)?

• √3/2

• 1

• √3

• 1/2

Which identity is used to simplify the expression 1 - cos²(x)?

• sin²(x)

• cos²(x)

• tan²(x)

• 1 + sin²(x)

How do you express tan(x) in terms of sine and cosine?

• cos(x)/sin(x)

• sin(x)/cos(x)

• sin(x) - cos(x)

• sin(x) + cos(x)

What is the result of the limit as x approaches 0 for (1 - cos(6x))/(1 - cos(2x))?

• 3

• 1/3

• 2

• 1/2

What is the limit as x approaches 0 for sin(7x) - sin(3x) divided by sin(2x)?

• 3

• 4

• 2

• 1

Which trigonometric identity is used to simplify 1 - cos(2x)?

• 2sin²(x)

• 2cos²(x)

• sin²(x)

• cos²(x)

What is the limit as x approaches 0 for tan²(x)/(6x²)?

• 1/12

• 1/6

• 1/18

• 1/36

What substitution is used to solve the limit as x approaches π/2 for sin(6x)/(x - π/2)?

• y = 2x - π

• y = x + π/2

• y = x - π/2

• y = 2x + π

How do you simplify the expression sin(3π + 6y)?

• sin(6y)

• -cos(6y)

• -sin(6y)

• cos(6y)

What is the limit as x approaches 3 for (x² - 9)/(sin(x - 3))?

• 6

• 1

• 0

• 3