Limit Properties and Evaluations

The video tutorial covers various methods to evaluate limits analytically, starting with the direct substitution property, which is applicable to continuous functions. It then explores properties of limits, such as scalar multiplication and sum/difference. Examples demonstrate direct substitution, and alternative methods like factoring and rationalizing are discussed for cases where direct substitution fails. Special limits, including sine and cosine limits, are also introduced.

What is the direct substitution property in evaluating limits?

• It involves graphing the function.

• It involves using L'Hôpital's rule.

• It involves substituting the limit value directly into the function.

• It involves finding the derivative of the function.

Which type of functions can the direct substitution property be applied to?

• Functions with discontinuities.

• Continuous functions like polynomials and sine functions.

• Piecewise functions.

• Functions with asymptotes.

What does the limit as x approaches c of a constant b equal?

• c

• Infinity

• b

• 0

What is the limit of x as x approaches c?

• 0

• x

• c

• Infinity

What is the scalar multiple property of limits?

• The limit of a product is the product of the limits.

• The limit of a sum is the sum of the limits.

• The limit of a quotient is the quotient of the limits.

• The limit of a function times a scalar is the scalar times the limit of the function.

How do you find the limit of a sum or difference of two functions?

• By finding the sum or difference of their limits.

• By subtracting their limits.

• By multiplying their limits.

• By dividing their limits.

What must be true for the quotient property of limits to apply?

• Both limits must be infinite.

• The numerator's limit must be zero.

• The denominator's limit must be infinite.

• The denominator's limit must not be zero.

What is the limit of a function raised to a power?

• The power of the limit of the function.

• The limit of the power of the function.

• The square root of the limit of the function.

• The reciprocal of the limit of the function.

What is the result of evaluating the limit as x approaches 1 of -3x^2 + x - 1 using direct substitution?

• 0

• 3

• 1

• -3

What should you try if direct substitution fails when evaluating a limit?

• Use L'Hôpital's rule.

• Try factoring or reducing.

• Graph the function.

• Use the power rule.