Trigonometric Functions and Limits

The video tutorial revisits the differentiation of trigonometric functions, emphasizing the textbook approach and the concept of limits. It introduces the Squeeze Law, using graph examples to explain its application in solving limits. The tutorial analyzes graph behavior, establishes inequalities, and applies the Squeeze Law to demonstrate its utility in proving limits. The session concludes with a recap of the Squeeze Law's significance in understanding trigonometric functions.

What is the derivative of the sine function?

• Tangent

• Sine

• Secant

• Cosine

Which approach involves looking at graphs to understand trigonometric derivatives?

• Graphical Approach

• Textbook Approach

• Algebraic Approach

• Numerical Approach

What is the purpose of the Squeeze Theorem in calculus?

• To find the maximum value of a function

• To determine the limit of a function

• To differentiate complex functions

• To integrate trigonometric functions

In the Squeeze Theorem, what happens if a function is squeezed between two equal values?

• The function becomes undefined

• The function oscillates

• The function equals the two values

• The function diverges

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

• Infinity

• Undefined

• 0

• 1

Which trigonometric function increases at a constant rate?

• Linear function x

• Cosine

• Tangent

• Sine

What is the behavior of tan(x) as it approaches its asymptote?

• It increases at an increasing rate

• It oscillates

• It remains constant

• It decreases

How do sin(x), x, and tan(x) behave for small values of x?

• They are approximately equal

• They oscillate

• They become undefined

• They diverge

What is the significance of the limit of x^2 - 4 over x - 2 as x approaches 2?

• It equals 2

• It equals 4

• It is undefined

• It equals 0

What is the result of applying the Squeeze Theorem to the limit of x/sin(x) as x approaches zero?

• The limit is undefined

• The limit is infinity

• The limit is 1

• The limit is 0