Saturday, February 1, 2014

Calculus and Its Applications, Chapter 1, 1.4, Section 1.4, Problem 36

Determine the f(x) of the function f(x)=11x

f(x+h)f(x)h=[11(x+h)][11x]h=11xh11xh=1x(1xh)(1x)(1xh)h=1x1+x+hh(1x)(1xh)=hh[1xhx+x2+xh]=112xh+x2+xh

Thus,

f(x)=limh0f(x+h)f(x)h=112x0+x2+x(0)=112x+x2

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