Calculus Answers

using MacLaurin Series: by mutiplying the series sinx and cosx and mutiplying the answer by 2, show that sin2x= 2sinxcosx?


please help me as soon as possible( thank you)

Water is flowing at the rate of
50 m3min from a concrete conical reservoir (vertex down) of
base radius 45 m and height 6 m. (a) How fast is the water level
falling when the water is 5 m deep? (b) How fast is the radius of
the water’s surface changing at that moment? Give your answer
in cmmin.

what is symmetric difference of two sets.explain with example.

Sir,please help me.calculate the following limit.
Lim x approaches 0"(a^2-b^2)/x"

if x^y.y^x=1 then find dy/dx

I need to find the double integral... I'll write it as it appears in my book, with the lower limit first

1.) Integral 1,4; Integral 0,y for the function (sqrt(x)) dx dy
2.) Integral -2,2; Integral -2,2 for the function (x+y) dy dx

Find relative extrema (if it exists) using first partials test of the following functions
1.) f(x,y)=xy
2.) f(x,y)=e^(-x^2-y^2)

I need to find the partial derivatives of the following functions
1.) f(x,y)=ln((x-y)/(x+y)^2)
2.) f(x,y)=ln(sqrt(xy))