calculus
limit of (|x+h|-|x|)/h as h goes to 0 at x=4
why is the answer 1?
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Answers
The answer is 1 because the limit of (|x+h|-|x|)/h as h approaches 0 gives the absolute value of the derivative of the function f(x)=|x| at x=4. Since this function is a piecewise linear function (abs(-x) for x<0 and abs(x) for x>=0) and its slope is 1 at x=4, the limit is equal to 1.
