Evaluating Limits and L'Hospital's Rule

What does L'Hospital's Rule help to determine?

• The integral of functions over an interval

• The limit of indeterminate forms like 0/0 or infinity/infinity

• The derivative of functions at a point

• The limit of functions as x approaches infinity

What is required for L'Hospital's Rule to be applied?

• Both functions must approach zero as x approaches a certain value

• Both functions must be integrable

• Both functions must be differentiable and approach zero or infinity

• The functions must be linear

What does the limit of sine x over x as x approaches zero equal?

• 0

• 1

• Undefined

• Infinity

What form does e^x over x^3 approach as x approaches infinity?

• 0/0

• Infinity/Infinity

• 1/Infinity

• Infinity/0

How many times can L'Hospital's Rule be applied to a limit?

• As many times as needed until the form is determinate

• Twice maximum

• Only once

• It cannot be applied to limits

In which case can L'Hospital's Rule not be applied?

• When the limit is indeterminate like 0/0

• Both B and C

• When either the numerator or denominator does not approach zero or infinity

• When the functions are not differentiable

What is the limit of x plus sine x over x plus cosine x as x approaches zero?

• 0

• 1

• Infinity

• Undefined

How can indeterminate products be handled using L'Hospital's Rule?

• By taking the derivative of the product directly

• By converting the product into a quotient

• By applying trigonometric identities

• By converting the product into a sum

What does the limit of x to the power of x as x approaches zero from the positive direction equal?

• Undefined

• Infinity

• 1

• 0

What is the result of applying L'Hospital's Rule to natural log of x over (one over x) as x approaches zero from the positive direction?

• -Infinity

• 1

• 0

• Infinity