Calculus Answers

 If z = f(x, y), where x = e^u + e^−v , y = e^−u − e^v , then find ∂(u,v)/∂(x,y) .

Let u = f(r, s), r = x + at, s = y + bt, where x, y, t are independent variables and, a and b are constants. Show that ∂u/∂t = a (∂u/∂x) + b (∂u/∂y)

 Discuss the continuity of f(x, y) = (x^4)(y^4)/(x2+y 2)^3 if (x, y) not equal to (0,0), 0 if (x, y) = (0,0) at(0, 0) 

 A vertical line passing through the point (1,2) intersects the X axis at A(a, 0) and Y axis at B(0, b). Find area of triangle of least area if a and b are positive.

A bike drove 30 miles during a one hour trip. Show that bike speed was equal to 30 mile / hour at least once during the trip.

Find the Mean value of the function f left parenthesis x right parenthesis space equals space x cubed space minus space 3 x squared over the interval [0, 5].

X^3-2y^3+xy(2x-y)+y(x-y)+1=0

The ends and sides of a thin copper bar (𝛼 2 = 1.14) of length 2 are insulated so that no heat can pass through them. Find the temperature 𝑢(𝑥,𝑡) in the bar if initially 𝑢(𝑥, 0) = { 60𝑥 0 < 𝑥 < 1 60(2 − 𝑥) 1 ≤ 𝑥 < 2

. Find the area of the region enclosed by the graphs of y = 3/x and y = 4-x

Find the area of the region enclosed by the graphs of f(x) = x^3 and and g(x) = x^2+2x.