Taylor's Theorem with remainder states that

provided **u** has two continuous derivatives with respect to **x** and

provided **u** has four continuous derivatives with respect to **x**.
Use these Taylor formulas
to derive the following difference quotient formulas.

In each formula, the term with argument is the truncation error; it
represents the
error incurred in approximating a derivative with a difference quotient,
assuming that all arithmetic is infinite precision. Assuming **u** has
three continuous derivatives with respect to **x**, use Taylor's Theorem
with remainder to show