Understanding Special Limits in Calculus

The video tutorial explains how to use special limits to determine additional limits. It covers two examples: the limit of sine 3x divided by x and the limit of sine x divided by 5x. The tutorial demonstrates how to manipulate functions to match the form of special limits, allowing for easier calculation of limits. Graphical verification is also provided to confirm the results.

What is the value of the special limit as x approaches zero for sine x divided by x?

• 3

• Undefined

• 0

• 1

In the limit of sine 3x divided by x as x approaches zero, why do we multiply by 3/3?

• To eliminate the sine function

• To change the function

• To make the input of sine match the denominator

• To simplify the expression

What is the final value of the limit of sine 3x divided by x as x approaches zero?

• 1

• 3

• 0

• 2

What does the graph of f(x) = sine 3x divided by x show as x approaches zero?

• The function value approaches 3

• The function value approaches 1

• The function value approaches 2

• The function value approaches 0

In the limit of sine x divided by 5x as x approaches zero, what is the role of the factor 1/5?

• It changes the limit

• It is a constant factor

• It simplifies the expression

• It matches the input of sine with the denominator

What is the final value of the limit of sine x divided by 5x as x approaches zero?

• 1/5

• 1

• 5

• 0

What does the graph of f(x) = sine x divided by 5x show as x approaches zero?

• The function value approaches 0

• The function value approaches 1

• The function value approaches 1/5

• The function value approaches 5

Why is it important for the input of the sine function to match the denominator in these limits?

• To simplify the calculation

• To make the function continuous

• To apply the special limit rule

• To ensure the limit is zero

What happens to the limit of sine x divided by x as x approaches zero if the input and denominator do not match?

• The limit is one

• The limit is undefined

• The limit is zero

• The limit is infinite

How can graphical verification help in understanding limits?

• It simplifies the calculation

• It shows the exact value of the limit

• It provides a visual confirmation

• It eliminates the need for algebra