Limits and Exponential Functions

The video tutorial explains how to evaluate limits at infinity using exponential functions. It covers two methods: simplifying the limit by ignoring negligible terms and dividing each term by the exponential function. The tutorial also addresses evaluating limits as x approaches negative infinity, demonstrating that exponential terms approach zero, leading to a limit of one-sixth.

What is the initial form of the function (1 - 2e^x) / (-3e^x + 6) as x approaches infinity?

• Infinity/Infinity

• 1/0

• 0/0

• Negative Infinity/Negative Infinity

In the first method, why can the terms '1' and '6' be ignored when x approaches infinity?

• They are constants and do not affect the limit.

• They are multiplied by e^x.

• They are negative.

• They approach zero.

What is the simplified limit of the function using the first method?

• 1/6

• 3/2

• 2/3

• 1/3

In the second method, what do we divide each term by to simplify the limit?

• e^x

• x

• 6

• 1

What happens to the term 1/e^x as x approaches infinity?

• It approaches infinity.

• It approaches 1.

• It approaches zero.

• It remains constant.

What is the result of the limit using the second method?

• 1/6

• 3/2

• 2/3

• 1/3

As x approaches negative infinity, what does e^x approach?

• One

• Negative Infinity

• Zero

• Infinity

What is the limit of the function as x approaches negative infinity?

• 1/3

• 1/6

• 2/3

• 3/2

Why do the exponential terms approach zero as x approaches negative infinity?

• They are multiplied by negative constants.

• They are constants.

• They are divided by e^x.

• e^x approaches zero.

What is the main takeaway from the video regarding limits at infinity?

• Only the second method is valid.

• Both methods are valid for determining limits.

• Only one method is valid.

• Limits cannot be determined.