Understanding Limits and Graphing Functions

The video tutorial explores the behavior of the function f(x) = 3sin(5x)/sin(2x) as x approaches zero. It examines the function's values from both negative and positive directions, showing that the limit approaches 7.5. The tutorial includes a graphical verification using a graphing calculator to visualize the function's behavior and confirm the limit. The function is not defined at x = 0, but the approach from both sides indicates the limit is 7.5.

What is the function f(x) defined as in the problem?

• 3 sine of 2x over sine of 5x

• 5 sine of 3x over sine of 2x

• 3 sine of 5x over sine of 2x

• 2 sine of 5x over sine of 3x

What is the value of f(x) when x is -0.1?

• 7.497375

• 7.239550

• 7.499974

• 7.500000

As x approaches 0 from the negative side, what does the function value approach?

• 7.0

• 7.5

• 8.0

• 6.5

What is the value of f(x) when x is 0.1?

• 7.500000

• 7.239550

• 7.497375

• 7.499974

As x approaches 0 from the positive side, what does the function value approach?

• 7.0

• 6.5

• 7.5

• 8.0

What conclusion is drawn about the limit of the function as x approaches 0?

• The limit is 8.0

• The limit is undefined

• The limit is 6.5

• The limit is 7.5

What tool is suggested to verify the limit visually?

• A protractor

• A compass

• A graphing calculator

• A ruler

What is the suggested y-range for graphing the function?

• -5 to 5

• -1 to 8

• 0 to 5

• 0 to 10

What happens to the function graph as x approaches 0?

• It oscillates

• It diverges

• It becomes undefined

• It approaches 7.5

What is the significance of the function not being defined at 7.5?

• It means the function is linear

• It means the function is discontinuous

• It means the function is continuous

• It means the function is periodic