Calculus Exam #2

[ 𝗖𝗵𝗮𝗽𝘁𝗲𝗿 𝟯: 3.2, 3.5, 3.6, 3.7 ] [ 𝗖𝗵𝗮𝗽𝘁𝗲𝗿 𝟰: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7 ]

What is a one-to-one function ( f )?

Basically a function w/ one solution/output to one input (og function definition).

What is an inverse function?

What are the two cancellation equations?

What do the two cancellation equations represent?

That a function and its inverse basically cancel each other out.

What are the three steps to finding the inverse function of a one-to-one function f ?

How do we obtain the graph of an inverse function?

What is the relationship of continuity to a function and its inverse function?

If f a one-to-one continuous function defined on an interval, then its inverse function f ^-1 is also continuous.

What are two derivative equations/definitions for an inverse function?

What is the logarithmic function with base a and its inverse?

What are the two cancellation equations when applied to the log function w/ base a and its inverse?

What is the multiplication law for logarithms?

What is the division law for logarithms?

What is the exponent law for logarithms?

What are two limits of logarithmic functions if a > 1?

What is the natural logarithm? (definition)

Logarithm w/ base e.

What is the natural logarithm? (equation/notation).

What is the inverse of the natural log function?

What are the two cancellation equations for the natural log function and its inverse?

What is the change of base formula?

What is the derivative of f(x) = log_ax and its two ways to write it?

What is the derivative of the natural log function ln x?

When do you use logarithmic differentiation?

When calculating derivatives of complicated functions involving products, quotients, or powers.

What are the three steps in logarithmic differentiation?

What is the derivative of an exponential function? (x is the exponent).

What is the derivative of a natural exponential function?

What are two ways to write the differential equations for the Law of Natural Growth/Decay?

What is the equation for population growth P(t)?

What are two ways to write the differential equations for radioactive decay?.

What is Newton's Law of Cooling?