Math Problem Statement
Find lim h -> 0 (f(x + h) - f(x))/h, when f(x) = x/(sqrt(1 + x))
Solution
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Math Problem Analysis
Mathematical Concepts
Limits
Derivatives
Quotient Rule
Square Roots
Difference Quotient
Formulas
Limit definition of a derivative: lim h -> 0 (f(x + h) - f(x))/h
Quotient rule: (u/v)' = (u'v - uv')/v^2
Square root approximations: sqrt(1 + x + h) ≈ sqrt(1 + x) as h -> 0
Theorems
Limit theorem
Quotient rule
Suitable Grade Level
Undergraduate Calculus