how we can use differentiation, Integration, Differentiability, Continuity, functions and Limits?
Needs: Step By Step Explaination!
how we can calculate the length of cable, an irregular/curved shape area using Calculus?
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Step-by-step explanation:
If a function f(x) is differentiable, then f'(x) may or may not be continuous, let alone differentiable. If f'(x) does happen to be continuous, we say f(x) is continuously differentiable. f(x) is differentiable everywhere, but f'(x)=|x|, which is continuous but not differentiable at 0.Imagine we want to find the length of a curve between two points. And the curve is smooth (the derivative is continuous).
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Example: Find the length of y = x(3/2) from x = 0 to x = 4.
u = 1 + (9/4)x.
du = (9/4)dx.
(4/9)du = dx.
Bounds: u(0)=1 and u(4)=10.
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