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Example 4
The absolute value function y = x is continuous but not differentiable at the point x = 0. (See Figure 3.4.4(b).) We have already shown that the derivative does not exist at x = 0. To see that the function is continuous, we note that for any infinitesimal Δx, Δy = 0 + Δx  0 = Δx and thus Δy is infinitesimal. Figure 3.4.4


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