The factory system began to emerge in the seventeenth century, when technological advances transformed the British textile industry.

Horizontal organization is

Beginning in the nineteenth century, industrializing lands experienced a social change known as the demographic transition when

Let V(x,y)=x2+y2-49{“version”:”1.1″,”math”:”V(x,y)=x2+y2-49″}, graph the boundary of the domain and shade the area of the boundary.  _______

Find the directional derivative of  at the point (3,3,-2){“version”:”1.1″,”math”:”(3,3,-2)”} in the direction u⇀=3i^-j^+4k^{“version”:”1.1″,”math”:”u⇀=3i^-j^+4k^”}.  (Hint:  You need to compute u⇀{“version”:”1.1″,”math”:”u⇀”} (in a unit vector) first.) _______

Consider a double integral ∫09∫x281ycos(y2) dydx{“version”:”1.1″,”math”:”∫09∫x281ycos(y2) dydx”}.  Draw the boundary area. If the order of integration was reversed, the double integral is ∫∫Rycos(y2) dxdy{“version”:”1.1″,”math”:”∫∫Rycos(y2) dxdy”}.  Determine the limits of integration. _____≤x≤_________,   ________≤y≤__________{“version”:”1.1″,”math”:”_____≤x≤_________,   ________≤y≤__________”} Now evaluate the integral.  Write the answer in exact form. _______

Find and classify the critical points of f(x,y)=-3+2x+4×2+4y-y2{“version”:”1.1″,”math”:”f(x,y)=-3+2x+4×2+4y-y2″}. _______

Find an equation for the tangent plane to the surface  z=5ycos(4x-3y){“version”:”1.1″,”math”:”z=5ycos(4x-3y)”}    at the point (3,4,20). _______

If g(x,y)=x2yx4+5y2{“version”:”1.1″,”math”:”g(x,y)=x2yx4+5y2″}, determine lim(x,y)→(0,0)g(x,y){“version”:”1.1″,”math”:”lim(x,y)→(0,0)g(x,y)”} by looking at various paths.  _______

Consider the following function f(x,y)=4x3y2-3xy5{“version”:”1.1″,”math”:”f(x,y)=4x3y2-3xy5″}. Find four second partial derivatives of f(x,y){“version”:”1.1″,”math”:”f(x,y)”}. _______