What differentiable functions have an arc length on the interval [a,b] given by the following integrals? Note that the answers are not unique. Give all functions that satisfy the conditions.
<h3>What are differentiable functions? </h3>
In mathematics, a differentiable function of one real variable is a function that has a derivative at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.
A smooth, differentiable function lacks any breaks, angles, or cusps (it is locally well approximated as a linear function at each interior point).
If the derivative f'(x 0) exists, a function f is said to be differentiable at x0 if x0 is an inner point in the domain of the function.
In other words, the point (x0, f(x0)) on the graph of f has a non-vertical tangent line. If f is differentiable at every point along U, then U is said to be differentiable.
If the derivative off is also a continuous function over the domain of the function ff, then f is said to be continuously differentiable.
In general, if f’s initial k derivatives are f prime (x), f prime (x), and lots, f(k)(x), then f is said to be of class Ck. f prime (x), f prime (x), lots, and f (k) prime (x) exist and are continuous across the function’s domain.
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