Exponential and Logarithmic Functions

The video tutorial explores the limits and continuity of exponential and logarithmic functions. It covers the natural exponential function y = e^x, discussing its graph, asymptotes, and behavior as x approaches infinity. The tutorial also examines exponential growth and decay, emphasizing the importance of understanding these graphs. Logarithmic functions are introduced, highlighting their properties and inverse relationship with exponential functions. The video concludes with examples demonstrating problem-solving techniques using limits and function properties.

What is the primary focus of the video tutorial?

• Limits and continuity of trigonometric functions

• Limits and continuity of exponential and logarithmic functions

• Graphing polynomial functions

• Solving quadratic equations

What is the base of the natural exponential function?

• Pi

• Euler's number (e)

• Infinity

• Zero

What is the approximate value of Euler's number (e)?

• 1.618

• 2.7

• 3.14

• 0

What happens to the value of e^x as x approaches negative infinity?

• It approaches infinity

• It approaches zero

• It becomes negative

• It remains constant

What is the horizontal asymptote of the exponential function y = e^x?

• y = 1

• y = x

• y = e

• y = 0

What is the value of e^0?

• Infinity

• e

• 1

• 0

What is the point on the graph of y = e^x when x = 1?

• (0, 1)

• (1, e)

• (e, 1)

• (1, 0)

What is the behavior of the function y = e^-x?

• Exponential growth

• Quadratic growth

• Exponential decay

• Linear growth

What is the domain of the exponential function y = e^x?

• All real numbers

• Only integers

• All positive real numbers

• All negative real numbers

What is the limit of e^x as x approaches positive infinity?

• Zero

• One

• Positive infinity

• Negative infinity