Questions from General Calculus

Q: Find the point on the line y = 2x + 3 that

Find the point on the line y = 2x + 3 that is closest to the origin.

Q: Find the points on the ellipse 4x2 + y2 = 4 that

Find the points on the ellipse 4x2 + y2 = 4 that are farthest away from the point (1, 0).

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 = sin x that is closest to the point (4, 2).

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 a circle of radius r.

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: Differentiate the function. g(x) = ln(

Differentiate the function. g(x) = ln(xe-2x)

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 area of the largest trapezoid that can be inscribed in

Find the area of the largest trapezoid that can be inscribed in a circle of radius 1 and whose base is a diameter of the circle.

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: If the two equal sides of an isosceles triangle have length a

If the two equal sides of an isosceles triangle have length a, find the length of the third side that maximizes the area of the triangle.