Use linear approximations to estimate the following quantities. Choose a value of a to produce a small error.
e⁰·⁰⁶

Verified step by step guidance

1. Identify the function to be approximated, which is f(x) = e^x, and the point a at which to approximate the function. A good choice for a is 0, since e^0 = 1 is easy to calculate.
2. Calculate the derivative of the function, f'(x) = e^x, which will be used for the linear approximation.
3. Evaluate the function and its derivative at the point a. For a = 0, find f(0) = e^0 = 1 and f'(0) = e^0 = 1.
4. Use the linear approximation formula, L(x) = f(a) + f'(a)(x - a), substituting in the values found: L(0.06) = 1 + 1(0.06 - 0) = 1 + 0.06.
5. Calculate the linear approximation to estimate e^0.06 using the expression from the previous step, which gives you an approximate value.