Home/Differential Calculus/Linear approximation/Formula10.2. Linear approximationFormulaIn 10.2. Linear approximationFormulaCopy LaTeX1+x≈1+x2,∣x∣≪1\sqrt{1+x}\approx 1+\frac{x}{2},\qquad |x|\ll11+x≈1+2x,∣x∣≪1TagsLinear approximationDifferential calculusDerivativeDifferentialDerivative formulaDetailClassic linear approximation.VariablesxxxIndependent variableConditions∣x∣≪1|x|\ll1∣x∣≪1Found an error? Contact us.Related formulasRelatedFormulaΔy≈f′(a) Δx\Delta y\approx f'(a)\,\Delta xΔy≈f′(a)ΔxOpen formulaOpen in sectionRelatedFormulaf(x)≈f(a)+f′(a)(x−a)when x≈af(x)\approx f(a)+f'(a)(x-a)\quad\text{when }x\approx af(x)≈f(a)+f′(a)(x−a)when x≈aOpen formulaOpen in sectionRelatedFormulaL(x)=f(a)+f′(a)(x−a)L(x)=f(a)+f'(a)(x-a)L(x)=f(a)+f′(a)(x−a)Open formulaOpen in section