Hyperbolic Functions and Their Properties

Professor Dave introduces hyperbolic functions, explaining their relation to hyperbolas and how they differ from trigonometric functions. He covers hyperbolic sine, cosine, tangent, and their reciprocals, discussing their properties, identities, and derivatives. The video also explores inverse hyperbolic functions, their graphical representation, and differentiation.

What is the primary difference between trigonometric and hyperbolic functions?

• Trigonometric functions are related to the hyperbola, while hyperbolic functions are related to the unit circle.

• Trigonometric functions are related to the unit circle, while hyperbolic functions are related to the hyperbola.

• Both are related to the unit circle.

• Both are related to the hyperbola.

How is hyperbolic sine expressed in terms of exponential functions?

• (E^X + E^-X) / 2

• (E^X - E^-X) / 2

• (E^X + E^-X) / 3

• (E^X - E^-X) / 3

What is the range of the hyperbolic cosine function?

• From -1 to 1

• From 1 to positive infinity

• From 0 to positive infinity

• All real numbers

What is the relationship between hyperbolic tangent and other hyperbolic functions?

• It is the sum of hyperbolic sine and cosine.

• It is the product of hyperbolic sine and cosine.

• It is the difference between hyperbolic sine and cosine.

• It is the ratio of hyperbolic sine to hyperbolic cosine.

Which hyperbolic function has horizontal asymptotes at -1 and 1?

• Hyperbolic secant

• Hyperbolic cosine

• Hyperbolic sine

• Hyperbolic tangent

What must be done to the domain of hyperbolic cosine to find its inverse?

• Restrict to greater than or equal to zero

• Restrict to positive numbers only

• Restrict to less than or equal to zero

• No restriction needed

How can inverse hyperbolic functions be expressed in terms of X?

• By swapping X and Y and solving for X

• By swapping X and Y and solving for Y

• By using the quadratic formula directly

• By taking the natural log of X

What is the first step in differentiating inverse hyperbolic sine?

• Use the quotient rule

• Use the power rule

• Use the chain rule

• Use the product rule

What is the derivative of E^X?

• 1/E^X

• X * E^X

• E^-X

• E^X

What is the final step in finding the derivative of inverse hyperbolic sine?

• Use the power rule

• Combine terms to simplify

• Apply the quotient rule

• Apply the product rule