Home/Differential Calculus/Limits at infinity/Formula2.6. Limits at infinityFormulaIn 2.6. Limits at infinityFormulaCopy LaTeXlimx→∞1xp=0,p>0\lim_{x\to\infty}\frac{1}{x^p}=0,\qquad p>0x→∞limxp1=0,p>0TagsDifferential calculusLimitLimits at infinityVariablesxxxIndependent variableConditionsp>0p>0p>0Found an error? Contact us.Related formulasRelatedFormulalimx→∞anxn+⋯+a0bmxm+⋯+b0={0,n<manbm,n=msgn (anbm)⋅∞,n>m\lim_{x\to\infty}\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots+b_0}= \begin{cases} 0, & n<m\\ \frac{a_n}{b_m}, & n=m\\ \operatorname{sgn}\!\left(\frac{a_n}{b_m}\right)\cdot\infty, & n>m \end{cases}x→∞limbmxm+⋯+b0anxn+⋯+a0=⎩⎨⎧0,bman,sgn(bman)⋅∞,n<mn=mn>mOpen formulaOpen in section