Determining Limits with Algebraic Properties

Mr. Bean introduces calculus students to the algebraic properties of limits, emphasizing their similarity to basic algebraic properties. Through examples, he demonstrates how to evaluate limits using tables, compositions, and piecewise functions. The lesson includes practical exercises to help students distinguish between limits and function values, and understand the behavior of functions as they approach specific values. The video concludes with practice problems to reinforce the concepts covered.

What is the result of adding the limits of f(x) as x approaches a constant c?

• The sum of the limits is zero.

• The sum of the limits is always one.

• The sum of the limits is undefined.

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

When evaluating the limit of f(x) as x approaches 1, what should you consider if the function is f(-x)?

• The limit as x approaches infinity.

• The limit as x approaches 0.

• The limit as x approaches -1.

• The limit as x approaches 1.

In a composition of functions, what is the first step to find the limit as x approaches a value?

• Evaluate the outer function first.

• Evaluate the inner function first.

• Add the limits of both functions.

• Subtract the limits of both functions.

What is the limit of f(x) as x approaches 4 if the inner function approaches 1?

• The limit is -1.

• The limit is 1.

• The limit is 4.

• The limit is 0.

How do you distinguish between the limit and the actual value of a function in a table?

• The limit and the actual value are always the same.

• The limit is always greater than the actual value.

• The limit is always less than the actual value.

• The limit is the value the function approaches, not necessarily the actual value.

What is the limit of h(x) as x approaches 5 if h(5) is 3?

• The limit is 3.

• The limit is 5.

• The limit is 6.

• The limit does not exist.

When dealing with piecewise functions, what does the minus symbol indicate?

• Approaching from both sides.

• Approaching from the left side.

• Approaching from the right side.

• Approaching from above.

What is the result of the limit as x approaches -5 from the left for the function sqrt(11 - x)?

• The result is -16.

• The result is 16.

• The result is -4.

• The result is 4.

What is the simplified result of the limit as x approaches -5 from the right for the function (x + 3) / (5 - x^2)?

• 1/2

• 1/5

• 1/10

• 1/20

What is the limit as x approaches -5 if the left and right limits are different?

• The limit is the product of the two.

• The limit does not exist.

• The limit is the sum of the two.

• The limit is the average of the two.