Questions from General Calculus

Q: The amount, A, of anesthetics that a certain hospital uses

The amount, A, of anesthetics that a certain hospital uses each week is a function of the number, S, of surgical operations performed each week. Also, S, in turn, is a function of the population, P, o...

Q: The graph of x2/3 + y2/3 = 8

The graph of x2/3 + y2/3 = 8 is the astroid in Fig. 3. (a) Find dy/dx by implicit differentiation. (b) Find the slope of the tangent line at (8, -8). Figure 3:

Q: Differentiate the function. y = x2 / (x2 +

Differentiate the function. y = x2 / (x2 + 1)2

Q: The graph of x3 + y3 = 9xy is the folium of

The graph of x3 + y3 = 9xy is the folium of Descartes shown in Fig. 4. (a) Find dy/dx by implicit differentiation. (b) Find the slope of the curve at (2, 4). Figure 4:

Q: x and y are related by the given equation. Use implicit

x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y. x2y2 = 9; x = 1, y = 3

Q: The body mass index, or BMI, is a ratio of

The body mass index, or BMI, is a ratio of a person’s weight divided by the square of his or her height. Let b (t) denote the BMI; then, b (t) = w(t) / [h(t)]2, where t is the age of the person, w(t...

Q: x and y are related by the given equation. Use implicit

x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y. xy4 = 48; x = 3, y = 2

Q: x and y are related by the given equation. Use implicit

x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y. x2 - xy3 = 20; x = 5, y = 1

Q: x and y are related by the given equation. Use implicit

x and y are related by the given equation. Use implicit differentiation to calculate the value of dy/dx for the given values of x and y. xy2 - x3 = 10; x = 2, y = 3

Q: A factory’s weekly production costs y and its weekly production quantity x

A factory’s weekly production costs y and its weekly production quantity x are related by the equation y2 - 5x3 = 4, where y is in thousands of dollars and x is in thousands of units of output. (a) Us...