MATH 1205 Midterm: MATH 1205 VT 1205c Test f f08

Suppose f(3) = 7, f'(1) - 6, g(-4) = 1, and g'(-4) = 5. If h(x)- f(g(x)), find h'(-4). If k(x) - ln (g(x)), find k'(-4). Given x2 + 2xy - y2 + x = 2, find an equation of the tangent line at (1,2).

Given that the area of the circular disk {(x, y) : x2 +y2 1} is equal to pi. find the areas of the elliptical disks given by: {(x, y): x2/4 + y2/9 1}; {{x, y) : 2x2 + 2xy + 5y2 1}. (Hint: 2x2 + 2xy + 5y2 = (x + 2y)2 + (x - y)2.)

Find y as a function of X if x 2 y " -2xy ' - 18y = x 5, y(1) = 3, y ' (1) = -2. y =