Limits and Trigonometric Functions

This video tutorial introduces the concept of limits in calculus, focusing on trigonometric functions like sine and cosine. It explains how to evaluate basic limits involving these functions and highlights the famous limit of sine of X over X. The tutorial also discusses the behavior of trigonometric functions and the challenges of dealing with limits that result in indeterminate forms like zero over zero.

What is the main focus of this lesson in calculus?

• Applications of calculus in physics

• Derivatives of polynomial functions

• Limits involving trigonometric functions

• Integration techniques

Which trigonometric functions are mentioned as examples in the introduction?

• Sine, cosine, and tangent

• Sine, tangent, and secant

• Cosine, cotangent, and cosecant

• Secant, cosecant, and cotangent

What is the limit of sine of x as x approaches zero?

• 1

• 0

• Infinity

• Undefined

How can you determine the behavior of the sine function near zero?

• By using a graphing calculator

• By applying the derivative

• By creating a table of values

• By using integration

What is the result of sine of zero?

• Infinity

• Undefined

• 0

• 1

What is the behavior of the sine function as x approaches zero?

• It approaches zero

• It approaches infinity

• It becomes undefined

• It becomes negative

What is a characteristic of the sine and cosine functions?

• They are discontinuous

• They are periodic

• They are not defined at zero

• They are not smooth

Why is the tangent function not continuous everywhere?

• It has infinities due to division by zero

• It is only defined for integer values

• It is not defined for negative values

• It is a piecewise function

What happens to the sine function as x approaches infinity?

• It approaches infinity

• It approaches zero

• It oscillates between -1 and 1

• It becomes undefined

What is the limit of cosine of x as x approaches zero?

• 0

• 1

• Undefined

• Infinity