Limits of Exponential and Logarithmic Functions

The video tutorial introduces exponential functions, explaining their notation and properties. It discusses the behavior of exponential functions with different base values, including graphing them as rising or falling curves. The tutorial explores the limits of exponential functions as x approaches various values, such as infinity and zero. It then introduces logarithmic functions, explaining their relationship with exponential functions and their properties. The video concludes with a discussion on the limits of logarithmic functions and proofs of key results.

What is the base in the expression A^B?

• B

• B^A

• A

• A^B

Which of the following is an example of an exponential function?

• 2x + 3

• log(x)

• x^2

• 2^x

What happens to the graph of a^x when A > 1?

• It oscillates

• It rises as x increases

• It remains constant

• It falls as x increases

What is the approximate value of the number E?

• 2.72

• 1.61

• 1.41

• 3.14

As x tends to infinity, what does 2^x approach?

• 1

• Infinity

• Negative Infinity

• 0

What is the limit of a^x as x tends to minus infinity when A > 1?

• Infinity

• 0

• 1

• A

What is the inverse of the exponential function a^x?

• x^a

• a^x

• log(x)

• a^(-x)

What is the natural logarithm of a number?

• Logarithm to base 10

• Logarithm to base 2

• Logarithm to base 1

• Logarithm to base E

Which law of logarithms states that log(xy) = log(x) + log(y)?

• Power Law

• Quotient Law

• Product Law

• Inverse Law

What is the limit of log(1 + x)/x as x tends to zero?

• E

• Infinity

• 1

• 0