Math Problem Statement

Find lim h -> 0 (f(x + h) - f(x))/h, when f(x) = x/(sqrt(1 + x))

Solution

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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