Questions from General Calculus

Q: Describe the Chain Rule for the composition of two differentiable functions in

Describe the Chain Rule for the composition of two differentiable functions in your own words.

Q: y = 5(2 – x3)4 Find the derivative

y = 5(2 – x3)4 Find the derivative of the function.

Q: The graphs of f and g are shown. Let h(

The graphs of f and g are shown. Let h(x) = f (g(x)) and s(x) = g( f (x)). Find each derivative, if it exists. If the derivative does not exist, explain why. Find h’ (3) Find sâ...

Q: The frequency F of a fire truck siren heard by a stationary

The frequency F of a fire truck siren heard by a stationary observer is Where ±v represents the velocity of the accelerating fire truck in meters per second. Find the rate of change of...

Q: The displacement from equilibrium of an object in harmonic motion on the

The displacement from equilibrium of an object in harmonic motion on the end of a spring is /

Q: A 15-centimeter pendulum moves according to the equation θ =

A 15-centimeter pendulum moves according to the equation θ = 0.2 cos 8t, where θ is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular di...

Q: A buoy oscillates in simple harmonic motion y = A cos ωt

A buoy oscillates in simple harmonic motion y = A cos ωt as waves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every...

Q: The normal daily maximum temperatures T (in degrees Fahrenheit) for

The normal daily maximum temperatures T (in degrees Fahrenheit) for Chicago, Illinois, are shown in the table. Use a graphing utility to plot the data and find a model for the data of the form T(t) =...

Q: The cost C (in dollars) of producing x units of

The cost C (in dollars) of producing x units of a product is C = 60x + 1350. For one week, management determined that the number of units produced x at the end of t hours can be modeled by x = -1.6t3...

Q: The number N of bacteria in a culture after t days is

The number N of bacteria in a culture after t days is modeled by Find the rate of change of N with respect to t when t = 0, (b) t = 1, (c) t = 2, (d) t = 3, and (e) t = 4. (f) what can you conclude?...