Questions from General Calculus

Q: (a) Graph several members of the family of functions f

(a) Graph several members of the family of functions f (x) = (2cx - x2)/c3 for c > 0 and look at the regions enclosed by these curves and the x-axis. Make a conjecture about how the areas of these reg...

Q: Find an equation for the surface consisting of all points P for

Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.

Q: Find dy/dx by implicit differentiation. x3 - xy2

Find dy/dx by implicit differentiation. x3 - xy2 + y3 = 1

Q: Differentiate. g(θ) = eθ (tanθ -

Differentiate. g(θ) = eθ (tanθ - θ)

Q: Let B be a solid box with length L, width W

Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L, W, and H.

Q: Let L be the line of intersection of the planes cx +

Let L be the line of intersection of the planes cx + y + z = c and x - cy + cz = 21, where c is a real number. (a). Find symmetric equations for L. (b). As the number c varies, the line L sweeps out a...

Q: A plane is capable of flying at a speed of 180 km

A plane is capable of flying at a speed of 180 km/h in still air. The pilot takes off from an airfield and heads due north according to the plane’s compass. After 30 minutes of flight time, the pilot...

Q: Find an equation of the largest sphere that passes through the point

Find an equation of the largest sphere that passes through the point (-1, 1, 4) and is such that each of the points (x, y, z) inside the sphere satisfies the condition x2 + y2 + z2, 136 + 2 (x + 2y +...

Q: A solid has the following properties. When illuminated by rays parallel

A solid has the following properties. When illuminated by rays parallel to the z-axis, its shadow is a circular disk. If the rays are parallel to the y-axis, its shadow is a square. If the rays are pa...

Q: Each edge of a cubical box has length 1 m. The

Each edge of a cubical box has length 1 m. The box contains nine spherical balls with the same radius r. The center of one ball is at the center of the cube and it touches the other eight balls. Each...