Find the tangent line approximation for near x = 0. What is the tangent line approximation to ex near x = 9? Find the tangent line approximation to 2/x near x = 2. What is the local linearization of near x = 1? The equation has a solution near x = 0. By replacing the left side of the equation by its linearization, find an approximate value for the solution. Writing g for the acceleration due to gravity, the period, T, of a pendulum of length I is given by Show that if the length of the pendulum changes by delta I, the change in the period, delta T, is given by If the length of the pendulum increases by 2%, by what percent does the period change? Suppose f'(x) is a differentiable decreasing function for all x. In each of the following pairs, which number is the larger?
