Calculus Answers

Find f_x(x,y), fy(x,y), f_x(1,3), and fy(-2,4) for the given function. If

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥³y² - 𝑥²y³ + 4𝑥 + 9

 Lim (3𝑥 − 𝑥 2 )

• Find the volume of the solid formed by revolving the curve, r=a(1+cosθ), about the initial line.

• Find the volume of the solid generated by revolving about the x-axis bounded by the curve, y2 = 9x and the line y = 3x

1. Find the area of the surface of the solid formed by the revolution the curve, x=a(θ - sinθ) and Y=a(1- cosθ) about x-axis (y=0).

• Show that the area bounded by the curve, (x/2)^2 /3 + (y/4)^2/3 = 1 is 3π.

• Find the volume of the solid generated by revolving the area enclosed between the evolute, 27ay^2 = 4(x-2a) ^3 and the parabola, y^2 = 4ax about x-axis.

A unique package is made up of cube with cylinder on top. The diameter of the cylinder equals the length of the cube. If the total volume is 50 cubic cm. What dimensions of the package will minimize the surface area of the package?

Determine the location and values of the absolute maximum and absolute 

minimum for the given function: 

F(x) = (−x + 2)

Power 4

, 𝑤ℎ𝑒𝑟𝑒 0 ≤ x ≤ 3

Use appropriate differentiation techniques to determine the first derivatives

1. "y=(3\u221ax -2xe^x)\/x"
2. "y=\ufeffcos(\u221asin(tan\u03c0x))"
3. "y=(tanx-1)\/secx"