Understanding Limits from Tables

What is the limit of sine(X)/X as X approaches zero?

• 0

• Infinity

• 1

• Does not exist

Why is the function sine(X)/X undefined at X = 0?

• Because sine(0) is undefined

• Because it results in division by zero

• Because X cannot be zero

• Because sine(X) is not defined for X = 0

What happens to the values of 1/(X-2)^3 as X approaches 2 from the left?

• They become large positive numbers

• They oscillate

• They remain constant

• They become large negative numbers

What is the behavior of 1/(X-2)^3 as X approaches 2 from the right?

• Values oscillate

• Values become large negative

• Values remain constant

• Values become large positive

What is the limit of (X^2-1)/(X-1) as X approaches 1?

• 0

• Does not exist

• 1

• 2

Why is there a hole in the graph of (X^2-1)/(X-1) at X = 1?

• Because X = 1 is not in the domain

• Because the graph is discontinuous

• Because the function is undefined at X = 1

• Because the limit does not exist

What is the behavior of sine(1/X) as X approaches zero?

• It oscillates rapidly

• It approaches a single value

• It becomes zero

• It becomes infinite

Why does the limit of sine(1/X) not exist as X approaches zero?

• Because it becomes infinite

• Because it oscillates too rapidly

• Because it becomes zero

• Because it approaches different values from each side

What is the key takeaway from the analysis of sine(1/X) as X approaches zero?

• The limit is infinite

• The limit does not exist due to oscillation

• The limit is zero

• The limit is one

What should you explore next after understanding limits from tables?

• Differential equations

• One-sided limits

• Integration

• Complex numbers