Understanding Limits and Asymptotes

The video tutorial explains the concept of limits using the function f(x) = 1/x. It explores limits as x approaches 0 from both positive and negative directions, showing that f(x) approaches positive and negative infinity, respectively. The tutorial also examines limits as x approaches positive and negative infinity, where f(x) approaches 0. A graphical representation of the function is provided, highlighting horizontal and vertical asymptotes. The video aims to build an intuitive understanding of limits without formal definitions.

What happens to f(x) as x approaches 0 from the positive direction?

• f(x) approaches 0

• f(x) approaches negative infinity

• f(x) approaches positive infinity

• f(x) remains constant

When x is negative and approaches 0, what is the behavior of f(x)?

• f(x) approaches negative infinity

• f(x) remains constant

• f(x) approaches positive infinity

• f(x) approaches 0

What is the behavior of f(x) as x approaches 0 from the negative direction?

• f(x) approaches positive infinity

• f(x) remains constant

• f(x) approaches negative infinity

• f(x) approaches 0

As x becomes very large, what does f(x) approach?

• Positive infinity

• Negative infinity

• Zero

• One

What is the limit of f(x) as x approaches negative infinity?

• Positive infinity

• Negative infinity

• Undefined

• Zero

What is a horizontal asymptote in the graph of f(x) = 1/x?

• y = infinity

• x = 0

• y = 0

• x = infinity

What is a vertical asymptote in the graph of f(x) = 1/x?

• y = infinity

• x = infinity

• y = 0

• x = 0

What does the graph of f(x) = 1/x look like as x approaches infinity?

• It forms a parabola

• It becomes a straight line

• It approaches a vertical line at x = 0

• It approaches a horizontal line at y = 0

What happens to f(x) as x becomes more negative?

• f(x) remains constant

• f(x) approaches 0

• f(x) approaches negative infinity

• f(x) approaches positive infinity

Why is the limit of f(x) as x approaches 0 not defined?

• Because f(x) approaches different values from positive and negative directions

• Because f(x) is undefined

• Because f(x) approaches the same value from both directions

• Because f(x) is constant