W. Rudin, Principles of Mathematical Analysis.
W. Fleming, Functions of Several Variables.
For the set of real numbers R, a function
f: R --> R
x in R, d in R, function f is differentiable at x with value d provided for h in R
lim_{h --> 0} (f(x + h) - f(x))/h = d
In this case we write
f'(x) = df(x)/dx = d
In that case, in particular,
lim_{h --> 0} (f(x + h) - f(x)) = 0
so that f is continuous at x.
Differentiation is important in physics, e.g., in Newton's second law.
W. Rudin, Principles of Mathematical Analysis.
W. Fleming, Functions of Several Variables.
For the set of real numbers R, a function
f: R --> R
x in R, d in R, function f is differentiable at x with value d provided for h in R
lim_{h --> 0} (f(x + h) - f(x))/h = d
In this case we write
f'(x) = df(x)/dx = d
In that case, in particular,
lim_{h --> 0} (f(x + h) - f(x)) = 0
so that f is continuous at x.
Differentiation is important in physics, e.g., in Newton's second law.