Understanding Limits and L'Hopital's Rule

The video tutorial explains how to find limits of functions as x approaches infinity, particularly when both the numerator and denominator approach infinity, resulting in an indeterminate form. L'Hopital's Rule is introduced as a method to solve these limits by using derivatives. Two examples are provided: one involving the natural log function and another with exponential functions. The tutorial also includes graphical verifications to confirm the calculated limits, demonstrating that the function values approach zero as x approaches infinity.

What is the indeterminate form discussed in the video when both the numerator and denominator approach infinity?

• Infinity over zero

• Zero over zero

• Zero over infinity

• Infinity over infinity

What rule is used to evaluate limits involving indeterminate forms?

• Bernoulli's Rule

• L'Hopital's Rule

• Newton's Rule

• Euler's Rule

In the first example, what is the derivative of the natural log of 2x?

• 2/(2x)

• 2/x

• 1/(2x)

• 1/x

What does the limit of 1/x approach as x approaches infinity?

• One

• Negative infinity

• Zero

• Infinity

How is the limit verified in the first example?

• By solving algebraically

• By using a graph

• By using a calculator

• By estimating

In the second example, what is the derivative of 2x cubed?

• 2x squared

• 3x squared

• 6x squared

• 6x

What happens to the fraction as the denominator increases without bound in the second example?

• It approaches zero

• It remains constant

• It becomes undefined

• It approaches infinity

How many times is L'Hopital's Rule applied in the second example?

• Four times

• Once

• Twice

• Three times

What is the final limit of the second example as x approaches infinity?

• Infinity

• Zero

• One

• Negative infinity

How is the limit verified in the second example?

• By using a calculator

• By estimating

• By solving algebraically

• By using a graph