Calculus Answers

Find the second partial derivative "\\displaystyle{\\frac{\\partial^2 z}{\\partial x^2}}" of the function "z=\\sin(xy^2)" at point "(\\pi, 1)"

True or False:

The mixed partial derivatives "\\displaystyle{\\frac{\\partial^2 z}{\\partial y \\partial x}}"  and "\\displaystyle{\\frac{\\partial^2 z}{\\partial x \\partial y}}"   are equal

Find the first partial derivative "\\displaystyle{\\frac{\\partial z}{ \\partial x}}" ​ of the function "z=x^2e^{-y}" at point  (2,-1)

Use cylindrical shells to find the volume of the solid that results when the red region is revolved about the y

y-axis. f(x)=x^2 ,a=1 ,b=4

The sides of a square are increasing at a rate of 10 cm/sec. How fast is the area enclosed by the square increasing when the area is 150 cm^2.

Show that 𝑈(−𝑓, 𝑝) = −𝐿(𝑓, 𝑝) and 𝐿(−𝑓, 𝑝) = −𝑈(𝑓, 𝑝)