Use the tangent line approximation to evaluate the following in two ways. First, find the tangent line to the whole function using the chain rule. Second, break the calculation into two pieces by writing the function as a composition, approximate the inner function with its tangent line, and use this value to plug into the tangent line of the outer function. Do your answers match?
1. (1 + 3 × 1.01)2
2. ln(√0.98)
3. esin(0.02)
4. sin (ln [(1 + 0.1 )3])