Questions from General Calculus

Q: Find, correct to two decimal places, the coordinates of the

Find, correct to two decimal places, the coordinates of the point on the curve y = tan x that is closest to the point (1, 1).

Q: Find the dimensions of the rectangle of largest area that can be

Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.

Q: Find the dimensions of the rectangle of largest area that has its

Find the dimensions of the rectangle of largest area that has its base on the -axis and its other two vertices above the x-axis and lying on the parabola y = 8 – x2.

Q: A right circular cylinder is inscribed in a sphere of radius r

A right circular cylinder is inscribed in a sphere of radius r. Find the largest possible volume of such a cylinder.

Q: Sketch the graph by hand using asymptotes and intercepts, but not

Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve...

Q: Find the area of the largest rectangle that can be inscribed in

Find the area of the largest rectangle that can be inscribed in the ellipse x2/a2 + y2/b2 = 1.

Q: Find the dimensions of the isosceles triangle of largest area that can

Find the dimensions of the isosceles triangle of largest area that can be inscribed in a circle of radius r.

Q: A cylindrical can without a top is made to contain V cm3

A cylindrical can without a top is made to contain V cm3 of liquid. Find the dimensions that will minimize the cost of the metal to make the can.

Q: A Norman window has the shape of a rectangle surmounted by a

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus, the diameter of the semicircle is equal to the width of the rectangle) If the perimeter of the window is 30 ft, find the...

Q: A right circular cylinder is inscribed in a cone with height and

A right circular cylinder is inscribed in a cone with height and base radius r. Find the largest possible volume of such a cylinder.