Home/Differential Calculus/Maclaurin formulas (a=0)/Formula11.2. Maclaurin formulas (a=0)FormulaIn 11.2. Maclaurin formulas (a=0)FormulaCopy LaTeXcosx=1−x22!+x44!−⋯\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdotscosx=1−2!x2+4!x4−⋯TagsDifferential calculusDerivativeDerivative formulaMaclaurin formulas (a=0)TaylorVariablesxxxIndependent variableFound an error? Contact us.Related formulasRelatedFormula\sinx=x−x33!+x55!−⋯\sinx=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\cdots\sinx=x−3!x3+5!x5−⋯Open formulaOpen in sectionRelatedFormulaln(1+x)=x−x22+x33−⋯ ,∣x∣<1\ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\cdots,\qquad |x|<1ln(1+x)=x−2x2+3x3−⋯,∣x∣<1Open formulaOpen in sectionRelatedFormulaex=1+x+x22!+x33!+⋯e^x=1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\cdotsex=1+x+2!x2+3!x3+⋯Open formulaOpen in sectionRelatedFormula(1+x)α=1+αx+α(α−1)2!x2+⋯ ,∣x∣<1(1+x)^\alpha=1+\alpha x+\frac{\alpha(\alpha-1)}{2!}x^2+\cdots,\qquad |x|<1(1+x)α=1+αx+2!α(α−1)x2+⋯,∣x∣<1Open formulaOpen in section