Understanding Limits of Composite Functions

This video tutorial covers how to find the limit of composite functions using various examples. It starts with a simple example using direct substitution with sine, then moves to more complex cases involving natural logarithms and cosine. The tutorial also explores limits involving tangent and exponential functions, emphasizing the importance of considering one-sided limits. The video concludes with a reminder to check both right and left-sided limits to determine if a limit exists.

What is the result of applying direct substitution to the limit of sine(x/3) as x approaches pi?

• Pi over 3

• Square root of 3 over 2

• 0

• 1

When evaluating the limit of ln(cos(x)) as x approaches zero, what is the result?

• Infinity

• Zero

• One

• Negative Infinity

What is the result of ln(1)?

• Undefined

• Zero

• One

• Negative Infinity

What is the value of cosine(0)?

• Zero

• One

• Negative One

• Undefined

In the example of ln(x cos(x)) as x approaches zero from the right, what is the final result?

• Negative Infinity

• Undefined

• Zero

• Positive Infinity

What is the limit of x as it approaches zero from the right?

• Zero

• Infinity

• One

• Negative One

What happens to the limit of e^(tan(x)) as x approaches pi/2 from the right?

• It approaches zero

• It approaches positive infinity

• It becomes undefined

• It approaches negative infinity

What is the limit of e^(tan(x)) as x approaches pi/2 from the left?

• Zero

• Undefined

• Negative Infinity

• Positive Infinity

Why is it important to consider one-sided limits when evaluating the limit of e^(tan(x))?

• Because the left and right limits are the same

• Because tangent is always positive

• Because tangent is undefined at 90 degrees

• Because tangent is always negative

What is the significance of the right and left-sided limits not being equal?

• The limit is infinite

• The limit exists

• The limit is zero

• The limit does not exist