(a) Let f be differential. Define a function f by the equation f*(x) = lim f(x+Ax)-f(x-Ax) Ax-0 Ax Find the relationship between f* and f. (b). Show that a differentiable function f(x) is continuous, i.e., lim f(x + Ax) = f(x). Ax-0

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Let f be differential. Define a function f by the equation
f(x+Ax)-f(x-Ax)
f*(x) = lim
Ax→0
Ax
Find the relationship between f* and f.
(b). Show that a differentiable function f(x) is continuous, i.e., lim f(x + Ax) = f(x).
Ax-0
Transcribed Image Text:(a) Let f be differential. Define a function f by the equation f(x+Ax)-f(x-Ax) f*(x) = lim Ax→0 Ax Find the relationship between f* and f. (b). Show that a differentiable function f(x) is continuous, i.e., lim f(x + Ax) = f(x). Ax-0
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