Calculus Answers

A box is to be made out of a piece of cardboard 38 cm x 38 cm, by cutting equal squares out of the

corners and turning up the sides. Find the volume of the largest box that can be made.

Albert builds rectangular pig pen with two parallel partitions using 300 meters of

fencing materials. What should be the dimensions of the pig pen so that it would enclose the largest

possible area?

Two jeepney leaves at the same terminal. Jeepney A heads North at a

constant speed of 40 ??/ℎ while jeepney B heads East at a constant

speed of 60 ??/ℎ. How fast is the distance between them changing

after 30 ?????

maximum or minimum of f(x, y) = x³+ y³– 63(x + y) + 12xy

Topic: Integration

Find the antiderivative of the following. Show your comple solution.

1.) Integral (6x⁵-4x²+2) dx

2.) Integral (12x²+2x) dx

3.) Integral 8^3/2 dx

4.) Integral 1/x¹² dx

5.) Integral ³√x dx

If I=V/R and V=250 volts and R=50ohms,find the change in I resulting from an increase of 2 volts in v and an increase of 0.5ohm in R. Using total differential method.

1.Find the area of the region that lies inside the circle r =3sinx and outside the cardioid

r = 1+sinx

Find the area of region y =17x²/16, y = 9x²/4 and y = 1 - 4x, satisfying x ≤0.

If f(x) = sin¹x, show that(1-x2)f"(x) xf'(x)