Consider finding an approximate solution to the nonlinear system of equations 2x1 − x22 = 0, x1 + 0.77x2 = 1, where x(0) = 0. (a) Apply one iteration of the Newton method to obtain x(1)

Suppose that T =f(t) gives the temperature T (in degrees Fahrenheit) of a pot of coffee t minutes after being brewed. If f '(20) = -3 and f(20) = 125, use a linear approximation (linearization) to estimate the coffee's temperature after 20.4 minutes.

Solve for x

A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the upper tap that feeds the water tank with a constant speed of v1 liters per minute and the lower tap that expels the water from the tank with a constant speed of v2 liters per minute . Suppose that v1 = 11 liters / minute and v2 = 3 liters / minute. If the tank has a capacity of 75 liters, when will the tank be filled?