Indeterminate Forms and Limit Evaluations

This video tutorial explains how to compute limits without using L'Hopital's Rule. It covers three limit problems involving trigonometric functions, demonstrating the use of known results and identities to evaluate limits. The video provides step-by-step solutions and alternative methods for solving indeterminate forms, emphasizing the importance of manipulation and substitution in limit evaluation. The tutorial concludes with a call to action for viewers to engage with the channel.

What is the value of cotangent x as x approaches 0 from the right?

• Negative infinity

• Positive infinity

• Zero

• One

What is the indeterminate form of the first limit problem?

• 0 × ∞

• 0/0

• ∞/∞

• 1/0

What is the limit of x cotangent x as x approaches 0?

• ∞

• 0

• 1

• Undefined

Why can't we use direct substitution for the second limit problem?

• Because tangent of 0 is undefined

• Because sine of 0 is undefined

• Because both tangent and sine of 0 are 0

• Because the limit does not exist

What is the indeterminate form of the second limit problem?

• ∞/∞

• 1/0

• 0/0

• 0 × ∞

What factor do we multiply by to make the product equal to the original expression in the second limit problem?

• 4/5

• 5/4

• 1/4

• 4/1

What is the final value of the second limit problem?

• 5/4

• 0

• 4/5

• 1

What is the limit of theta over theta as theta approaches 0?

• Undefined

• ∞

• 0

• 1

What is the indeterminate form of the third limit problem?

• 0/0

• ∞/∞

• 0 × ∞

• 1/0

What is the final value of the third limit problem?

• 0

• 1

• Undefined

• ∞