Understanding Limits and L'Hôpital's Rule

The video tutorial explains how to determine the exact value of a limit as x approaches infinity. It begins by analyzing the form of the limit and identifying it as an indeterminate form. The tutorial then applies L'Hôpital's Rule to solve the limit, simplifying the expression and using differentiation to find the final solution. The process involves factoring, using arithmetic properties, and applying calculus rules to reach the conclusion that the limit equals 3.

What is the initial form of the limit problem discussed in the video?

• 3x e^(x) - 3x

• 3x + e^(1/x)

• 3x e^(1/x) - 3x

• 3x e^(1/x) + 3x

As X approaches infinity, what does 1/X approach?

• One

• Infinity

• Zero

• Negative infinity

What is the indeterminate form identified in the problem?

• Infinity/Infinity

• Infinity - Infinity

• 0 * Infinity

• 0/0

What common factor is factored out from the terms in the expression?

• e^(1/x)

• 1/X

• 3

• X

How is multiplying by X rewritten in the expression?

• Multiplying by X^2

• Dividing by 1/X

• Multiplying by 1/X

• Dividing by X

What rule is applied to solve the indeterminate form?

• Chain Rule

• L'Hôpital's Rule

• Product Rule

• Quotient Rule

What is the derivative of 1/X with respect to X?

• 1/X^2

• -X^2

• -1/X^2

• X^2

After applying L'Hôpital's Rule, what does the expression simplify to?

• 3 * e^(1/X)

• 3 - e^(1/X)

• 3 + e^(1/X)

• 3 * X

As X approaches infinity, what does e^(1/X) approach?

• Infinity

• e

• 0

• 1

What is the final value of the limit?

• 0

• 1

• 3

• Infinity