To find the limit of (sqrt{x+h}- sqrt{x})/h as h approaches 0, you can rationalize the numerator. This is done by multiplying both the numerator and denominator by sqrt{x+h}+ sqrt{x}.
This operation yields ((sqrt{x+h}- sqrt{x})(sqrt{x+h}+sqrt{x}))/h(sqrt{x+h}+ sqrt{x}), which simplifies to (x+h- x)/(h(sqrt{x+h}+ sqrt{x})), which further simplifies to h/(h(sqrt{x+h}+ sqrt{x})), and ultimately, 1/(sqrt{x+h}+ sqrt{x}).
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