Limits and Trigonometric Functions

This video tutorial explains how to evaluate limits of trigonometric functions, focusing on two key formulas: the limit of sine x over x as x approaches 0 is 1, and the limit of 1 minus cosine x over x as x approaches 0 is 0. The video provides proofs for these formulas and demonstrates their application through various examples, including limits involving sine, cosine, and tangent functions. The tutorial emphasizes understanding the process of evaluating these limits and provides step-by-step solutions to enhance comprehension.

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

• Undefined

• Infinity

• 1

• 0

Which formula is used to evaluate the limit of sin(x)/x as x approaches 0?

• sin(x)/x = 1

• sin(x)/x = 0

• sin(x)/x = Undefined

• sin(x)/x = Infinity

What is the value of sin(0.1)/0.1 approximately?

• 1.0002

• 1.002

• 0.9998

• 0.998

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

• 0

• 1

• Infinity

• Undefined

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

• Undefined

• Infinity

• 1

• 0

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

• 0

• 1

• Infinity

• Undefined

What is the value of 1-cos(0.1)/0.1 approximately?

• 0.5

• 0.0005

• 0.005

• 0.05

What is the value of 1-cos(0.01)/0.01 approximately?

• 0.05

• 0.5

• 0.005

• 0.0005

What is the value of 1-cos(0.001)/0.001 approximately?

• 0.5

• 0.0005

• 0.005

• 0.05

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

• Infinity

• Undefined

• 1

• 0