There are six limit rules for the algebraic functions in calculus and they’re used as formulas to find the limits of algebraic functions. One limit rule is purely in algebraic form, another one rule is in logarithmic form and remaining formulas are in exponential form.

$(1) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, a}{\normalsize \dfrac{x^n-a^n}{x-a}}$ $\,=\,$ $na^{n-1}$

$(2) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{\log_{e}{(1+x)}}{x}}$ $\,=\,$ $1$

$(3) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{a^x-1}{x}}$ $\,=\,$ $\log_{e}{a}$

$(4) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{e^x-1}{x}}$ $\,=\,$ $1$

$(5) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize {(1+x)}^{\frac{1}{x}}}$ $\,=\,$ $e$

$(6) \,\,\,$ $\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize {\Bigg(1+\dfrac{1}{x}\Bigg)}^x}$ $\,=\,$ $e$

List of solved problems for evaluating limits of algebraic functions by using limit formulas for learning and practicing.

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Jul 29, 2022

Jul 17, 2022

Jun 02, 2022

Apr 06, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved