Questions from General Calculus

Q: What is the difference between a natural logarithm and a common logarithm

What is the difference between a natural logarithm and a common logarithm?

Q: Give the formula that converts a function of the form bx to

Give the formula that converts a function of the form bx to an exponential function with base e.

Q: If f (x) and g (x) are differentiable

If f (x) and g (x) are differentiable functions such that f (2) = f ‘(2) = 3, g (2) = 3, and g’(2) = 1/3, compute the derivative: d/dx [x f (x)] |x=2

Q: State the differentiation formula for each of the following functions (

State the differentiation formula for each of the following functions (a) f (x) = ekx (b) f (x) = eg(x) (c) f (x) = ln g(x)

Q: State the four algebraic properties of the natural logarithm function.

State the four algebraic properties of the natural logarithm function.

Q: Give an example of the use of logarithmic differentiation.

Give an example of the use of logarithmic differentiation.

Q: Differentiate the function using one or more of the differentiation rules discussed

Differentiate the function using one or more of the differentiation rules discussed thus far. y = 2(2x - 1)5/4 (2x + 1)3/4

Q: State as many laws of exponents as you can recall.

State as many laws of exponents as you can recall.

Q: What is e?

What is e?

Q: Write the differential equation satisfied by y = Cekt.

Write the differential equation satisfied by y = Cekt.