Understanding One-Sided Limits

The video tutorial explores the one-sided limits of the function f(x) = -1/(x-1)^2 as x approaches 1. It examines the behavior of the function from both the right and left sides, demonstrating that the function approaches negative infinity in both cases. The tutorial concludes by explaining the reasoning behind this behavior, emphasizing the constant numerator and the squared denominator, which results in a negative value for all x except x=1, where the function is undefined.

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

• f(x) = -1 / (x - 1)^2

• f(x) = -1 / (x + 1)^2

• f(x) = 1 / (x - 1)^2

• f(x) = 1 / (x + 1)^2

What happens to the limit of f(x) as x approaches 1 from the right?

• It approaches positive infinity.

• It approaches zero.

• It remains constant.

• It approaches negative infinity.

When x is 1.01, what is the value of f(x)?

• 100

• -100

• -10,000

• 10,000

As x approaches 1 from the left, what is the behavior of f(x)?

• It approaches zero.

• It approaches positive infinity.

• It remains constant.

• It approaches negative infinity.

What is the value of f(x) when x is 0.99?

• -100

• -10,000

• 100

• 10,000

What is the overall conclusion about the limits of f(x) as x approaches 1 from both sides?

• The limit is positive infinity.

• The limit is undefined.

• The limit is zero.

• The limit is negative infinity.

What is the nature of the numerator in the function f(x)?

• It is always negative.

• It is always positive.

• It varies with x.

• It is zero.

Why is the function f(x) not defined at x = 1?

• The numerator becomes zero.

• The denominator becomes zero.

• Both numerator and denominator become zero.

• The function is always defined.

What happens to the sign of the denominator when x approaches 1?

• It becomes positive.

• It remains zero.

• It becomes negative.

• It changes randomly.

What is the final deduction about the function's values as x approaches 1?

• The function can have zero values.

• The function can only have negative values.

• The function can have both positive and negative values.

• The function can have positive values.