Understanding Infinite Limits and Vertical Asymptotes

The video tutorial covers the concept of infinite limits, evaluating limits of functions like 1/x and 1/x^2 as x approaches zero, and provides examples of one-sided limits. It also explores limits involving trigonometric functions such as tangent and cosecant, and explains how to find vertical asymptotes in rational functions.

What is the limit of 1/x as x approaches zero from the left?

• Does not exist

• Zero

• Negative infinity

• Positive infinity

When evaluating the limit of 1/x^2 as x approaches zero from either side, what is the result?

• Does not exist

• Zero

• Negative infinity

• Positive infinity

What is the limit of 1/(x-2) as x approaches 2 from the left?

• Does not exist

• Zero

• Negative infinity

• Positive infinity

As x approaches pi/2 from the right, what is the behavior of the tangent function?

• Approaches zero

• Approaches positive infinity

• Approaches negative infinity

• Does not exist

What is the limit of cosecant x as x approaches zero from the right?

• Negative infinity

• Does not exist

• Positive infinity

• Zero

What happens to the limit of ln(x) as x approaches zero from the right?

• Approaches positive infinity

• Approaches negative infinity

• Approaches zero

• Does not exist

What is the limit of secant x as x approaches pi/2 from the left?

• Positive infinity

• Does not exist

• Negative infinity

• Zero

How do you find the vertical asymptote of a function like 1/(x+2)?

• Integrate the function

• Set the numerator to zero

• Set the denominator to zero

• Find the derivative

What is the vertical asymptote of the function 1/(x^2 - 4)?

• No vertical asymptote

• x = 0

• x = 4 and x = -4

• x = 2 and x = -2

In the function 1/(x^2 - 4), what technique is used to find the vertical asymptotes?

• Completing the square

• Difference of squares

• Quadratic formula

• Synthetic division