Estimating Limits from Tables

What is the main purpose of switching the calculator's table setting from Auto to Ask?

• To allow manual input of x-values

• To graph the function

• To automatically generate x-values

• To convert fractions to decimals

When estimating limits, why is it important to check both the left and right sides?

• To confirm the limit exists and is the same from both sides

• To ensure the function is continuous

• To find the exact value of the limit

• To verify the function is differentiable

What does the notation 1.4e-4 represent in calculator outputs?

• 1.4 times 10 to the power of 4

• 1.4 divided by 10 to the power of 4

• 1.4 times 10 to the power of -4

• 1.4 divided by 10 to the power of -4

Why do the y-values appear equal and opposite around x = 2 in the function (x - 2)/ln|x - 2|?

• Because the function is undefined at x = 2

• As a result of rounding errors

• Because the function is linear

• Due to the function's symmetry around x = 2

What is the significance of using three values on each side of the target x-value when estimating limits?

• To verify the function is differentiable

• To provide a more accurate estimate of the limit

• To ensure the function is continuous

• To simplify the calculation process

Why might a function not be defined at a certain point, yet still have a limit there?

• The function is undefined everywhere

• The function is differentiable at that point

• The function has a removable discontinuity

• The function is continuous at that point

Why is it important to use sufficiently small x-values when estimating limits near zero?

• To simplify the function

• To overpower large constants in the function

• To ensure the function is continuous

• To avoid calculator errors

What happens to the limit of the function as x approaches 0 from the right side in the discussed example?

• It approaches negative infinity

• It approaches zero

• It approaches positive infinity

• It remains constant

What is the effect of a vertical asymptote on the limit of a function?

• The limit is always positive

• The limit is always zero

• The limit is always negative

• The limit does not exist

What is the main takeaway regarding the use of tables for estimating limits?

• Tables provide exact values for limits

• Tables are the most reliable method for finding limits

• Tables are useful for estimation but analysis is more reliable

• Tables are only useful for continuous functions