Questions from General Calculus

Q: Show that the inflection points of the curve y = (sin

Show that the inflection points of the curve y = (sin x)/x lie on the curve y2 (x4 + 4) = 4.

Q: A particle moves with position function s = t4 - 4t3

A particle moves with position function s = t4 - 4t3 - 20t2 + 20t t ≥ 0 (a) At what time does the particle have a velocity of 20 m/s? (b) At what time is the acceleration 0? What is the significance o...

Q: Find the point on the parabola y = 1 - x2 at

Find the point on the parabola y = 1 - x2 at which the tangent line cuts from the first quadrant the triangle with the smallest area.

Q: Find an equation for the surface obtained by rotating the line z

Find an equation for the surface obtained by rotating the line z = 2y about the z-axis.

Q: (a) A company makes computer chips from square wafers of

(a) A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the si...

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

Find an equation for the surface consisting of all points that are equidistant from the point s21, 0, 0d and the plane x = 1. Identify the surface.

Q: The figure shows a parabolic segment, that is, a portion

The figure shows a parabolic segment, that is, a portion of a parabola cut off by a chord AB. It also shows a point C on the parabola with the property that the tangent line at C is parallel to the ch...

Q: Given the point (a,b) in the first quadrant

Given the point (a,b) in the first quadrant, find the downward-opening parabola that passes through the point (a,b) and the origin such that the area under the parabola is a minimum.

Q: The figure shows a region consisting of all points inside a square

The figure shows a region consisting of all points inside a square that are closer to the center than to the sides of the square. Find the area of the region.

Q: Find the minimum value of the area of the region under the

Find the minimum value of the area of the region under the curve y = x + 1/x from x = a to x = a + 1.5, for all a > 0.