Questions from General Calculus

Q: Find the highest and lowest points on the curve x2 + xy

Find the highest and lowest points on the curve x2 + xy + y2 = 12.

Q: A triangle with area is cut from a corner of a square

A triangle with area is cut from a corner of a square with side 10 cm, as shown in the figure. If the centroid of the remaining region is 4 cm from the right side of the square, how far is it from the...

Q: Suppose the graph of a cubic polynomial intersects the parabola when y

Suppose the graph of a cubic polynomial intersects the parabola when y = x2, x = 0, x = a and x = b, where 0 < a < b. If the two regions between the curves have the same area, how is b related to a?

Q: Evaluate the integral. f12 (2x – ex) dx

Evaluate the integral. f12 (2x – ex) dx

Q: Determine the values of the number for which the function f has

Determine the values of the number for which the function f has no critical number:

Q: Evaluate f∞-1(x4/1 + x6) dx

Evaluate f∞-1(x4/1 + x6) dx.

Q: Suppose f is continuous, f (0) = 0,

Suppose f is continuous, f (0) = 0, f (1) = 1, f'(x) > 0, and f10f (x) dx = 1/3. Find the value of the integral f10f-1 (y) dy.

Q: Evaluate f10(3√1 – x7 - 7√1

Evaluate f10(3√1 – x7 - 7√1 – x3) dx.

Q: Boxes are labeled as containing 500 g of cereal. The machine

Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces weights that are normally distributed with standard deviation 12 g. (a). If the target weight is 500 g, what is...

Q: (a). Let An be the area of a polygon with

(a). Let An be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle 2Ï€/n, show that (b). Sho...