Limits and Behavior of Exponential Functions

The video tutorial explains how to evaluate limits at infinity using two methods. The first method involves simplifying the limit by ignoring terms that have negligible impact as x approaches infinity. The second method involves dividing each term by the highest power of x in the denominator. The tutorial also covers evaluating the limit as x approaches negative infinity, showing that the limit approaches a constant value. Both methods are valid approaches to determine the limits, and the tutorial provides a clear explanation of each step involved.

What is the form of the limit when both the numerator and denominator approach infinity?

• Zero divided by infinity

• Zero

• Infinity divided by zero

• Infinity divided by infinity

Why can the constant 5 be ignored in the numerator as x approaches infinity?

• Because it is multiplied by e^x

• Because it approaches zero

• Because it does not affect the limit

• Because it is a negative number

How can e^x divided by e^(2x) be simplified?

• e^(2x-x)

• e^(x-2x)

• e^(x+2x)

• e^(x*x)

What is the result of simplifying 3 divided by (2 * e^x) as x approaches infinity?

• 3

• Infinity

• 2

• Zero

What is the alternative method for determining the limit?

• Multiplying every term by e^(2x)

• Dividing every term by e^(2x)

• Subtracting e^(2x) from every term

• Adding e^(2x) to every term

What happens to 5/e^(2x) as x approaches infinity?

• It approaches infinity

• It approaches zero

• It remains constant

• It approaches five

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

• Infinity

• Five-sevenths

• Seven-fifths

• Zero

How does e^x behave as x approaches negative infinity?

• It remains constant

• It approaches infinity

• It approaches zero

• It becomes negative

What is the behavior of 2e^(2x) as x approaches negative infinity?

• It approaches zero

• It becomes negative

• It approaches infinity

• It remains constant

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

• Five-sevenths

• Infinity

• Zero

• Seven-fifths