x 0 2 3 4

g'(x) 0.5 3 3.2 3.6

a. Use a local linear approximation to g at x=0 to approximate g(0.1)

b. Use a trapezoidal sum with the three subintervals from the table to

approximate integral g'(x) dx from 0 to 4. Use the approximation to estimate the value

of g(4).

c. Use Euler's method with two steps of equal size, starting at x=0, to approximate g(4).

Is the actual value of g(4) greater than or less than the approximation? Explain.

d. Integration by parts can be used to show that there is a function h such that integral x*g(x)*g'(x^2) dx=h(x)-12 * integral g'(x)*g(x^2)dx. Write an expression for h(x) involving no integrals.