Understanding Limits and Function Evaluation

The video tutorial explores the function f(x) = x^2 / (1 - cos(x)) and its behavior as x approaches zero from the positive side. It begins with a table of function values, highlighting a missing value. The instructor uses a calculator to evaluate the function at x=0.1, rounding the result to the nearest thousandth. The concept of a one-sided limit is discussed, with the limit approaching 2 as x nears zero. A graphing calculator is used to visualize the function, confirming the limit from both positive and negative directions. The tutorial concludes with observations on the function's behavior.

What is the function f(x) discussed in the video?

• f(x) = x^2 + cos(x)

• f(x) = x^2 / (1 - cos(x))

• f(x) = x^2 * (1 - cos(x))

• f(x) = x^2 - cos(x)

What is the missing value in the table evaluated at x = 0.1?

• 2.005

• 2.175

• 2.007

• 2.002

As x approaches zero from the positive direction, what does the limit of f(x) appear to be?

• 1

• 2

• 0

• 3

Why is it important to ensure the calculator is in radian mode?

• To display results in degrees

• To make calculations faster

• To avoid getting a strange answer

• To use less battery

What is the rounded value of f(x) at x = 0.1?

• 2.004

• 2.002

• 2.003

• 2.001

What tool is used to visualize the function graphically?

• Scientific calculator

• Graphing calculator

• Spreadsheet software

• Programming language

What is the maximum x value set for the graphing range?

• 2

• 1

• 0.5

• 1.5

What is the y maximum value set for the graph?

• 5

• 3

• 4

• 2

What does the graph show about the function's behavior as x approaches zero?

• It approaches 0

• It approaches 1

• It approaches 3

• It approaches 2

In which direction is the limit being evaluated in this problem?

• From the positive direction

• From both directions

• From the negative direction

• From the left