a. Confirm that the linear approximation to f(x) = tanh x at a = 0 is L(x) = x.

b. Recall that the velocity of a surface wave on the ocean is In fluid dynamics, shallow water refers to water where the depth-to-wavelength ratio d/λ < 0.05. Use your answer to part (a) to explain why the shallow water velocity equation is v = √gd.

c. Use the shallow-water velocity equation to explain why waves tend to slow down as they approach the shore.

g tanh 2d 2