Exploring Euler's Number and Logarithms

What is the base of natural logarithms commonly represented by?

• log

• e

• pi

• ln

What value does e approximately equal to?

• 1.62

• 2.71

• 1.41

• 3.14

What happens to the future value of an investment as the number of compounding periods per year increases?

• Becomes zero

• Increases

• Stays the same

• Decreases

What is the result of the expression (1 + 1/n)^n as n approaches infinity?

• 1

• e

• 0

• pi

What does the limit of (1 + n)^(1/n) approach as n approaches zero?

• 0

• 1

• infinity

• e

How is e approximated using a series expansion involving factorials?

• Product of 1 over n!

• Sum of n squared

• Product of n terms

• Sum of 1 over n!

What is the derivative of the function y = e^x?

• 1/e

• e

• x^e

• e^x

What does the area under the curve from negative infinity to x for the function y = e^x equal?

• e^x

• e

• x^e

• 1/e

What is the value of e to the negative infinity?

• e

• infinity

• 1

• 0

What is the geometric interpretation of the integral of e^x from negative infinity to x?

• Slope of the tangent equals e^x

• Area under the curve equals x

• Slope of the tangent equals x

• Area under the curve equals e^x