Math Doubts

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{e^x-1-x}{x^2}}$

The limit of natural exponential function in $x$ minus one minus $x$ divided by $x$ square should be evaluated in this limit problem as the value of $x$ approaches zero. Firstly, let us try to find the limit of rational function by the direct substitution.

$=\,\,$ $\dfrac{e^0-1-0}{0^2}$

According to the zero power rule, the mathematical constant $e$ raised to the power of zero is one.

$=\,\,$ $\dfrac{1-1-0}{0}$

$=\,\,$ $\dfrac{1-1}{0}$

$=\,\,$ $\dfrac{0}{0}$

According to the direct substitution, the limit $e$ raised to the power of $x$ minus $1$ minus $x$ divided by square of $x$ is indeterminate. So, we must think about other methods to find its limit. The limit of the given rational function can be evaluated in the following methods possibly.

L’Hôpital’s Rule

Evaluate $\displaystyle \large \lim_{x\,\to\,0}{\normalsize \dfrac{e^x-1-x}{x^2}}$

Learn how to find the limit of $e$ raised to the power of $x$ minus $1$ minus $x$ divided by $x$ square by the l’hospital’s rule.

Math Doubts

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

Maths Topics

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

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved