Limits of Trigonometric Functions

The video tutorial covers evaluating limits involving trigonometric functions, focusing on sine and cosine. It introduces basic limit equations, such as the limit of sine x over x as x approaches zero, and demonstrates techniques for evaluating these limits using substitution and calculators. The tutorial also explores complex limit problems and special cases, providing step-by-step solutions and explanations to enhance understanding.

What is the limit of sin(x)/x as x approaches 0?

• 0

• Undefined

• 1

• Infinity

How can you verify the limit of sin(x)/x using a calculator?

• By setting the calculator to degree mode

• By using the cosine function

• By plugging in values close to 0

• By plugging in values far from 0

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

• 1

• 0

• Undefined

• Infinity

What is the result of the limit of sin(5x)/x as x approaches 0?

• 5

• Undefined

• 1

• 0

How do you find the limit of sin(2x)/(5x) as x approaches 0?

• By using the tangent function

• By using substitution

• By dividing by 2

• By multiplying by 5

What is the limit of sin(7x)/sin(3x) as x approaches 0?

• 3/7

• 7/3

• 1

• 0

What is the limit of tan(x)/x as x approaches 0?

• Undefined

• Infinity

• 1

• 0

What is the limit of tan(4x)/(3x) as x approaches 0?

• 0

• 1

• 3/4

• 4/3

How do you simplify the limit of sin^2(x)/x as x approaches 0?

• By separating into two limits

• By using the identity sin^2(x) = 1 - cos^2(x)

• By multiplying by x

• By using the tangent function

What is the limit of sin(x^2)/x as x approaches 0?

• Infinity

• 0

• 1

• Undefined