The limit of sine of angle $x$ minus $1$ by $x$ square minus $1$ as $x$ approaches to $1$ is written in mathematical form as follows.

$\displaystyle \large \lim_{x\,\to\,1}{\normalsize \dfrac{\sin{(x-1)}}{x^2-1}}$

Firstly, use the direct substitution to find the limit of sine of angle $x$ minus $1$ by $x$ square minus $1$ as the value of $x$ is closer to $1$.

$=\,\,\,$ $\dfrac{\sin{(1-1)}}{1^2-1}$

$=\,\,\,$ $\dfrac{\sin{(0)}}{1-1}$

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

It is evaluated that the limit of sine of $x$ minus $1$ by square of $x$ minus $1$ is indeterminate as the value of $x$ approaches to $1$ as per the direct substitution. So, the direct substitution method is not useful to find the limit. However, the limit of sine of angle $x$ minus one by $x$ squared minus $1$ can be calculated by the following two methods.

Learn how to evaluate the limit of sine of $x$ minus $1$ by square of $x$ minus $1$ as the value of $x$ tends to $1$ by factorization (or factorisation).

Learn how to find the limit of sine of angle $x$ minus $1$ by $x$ square minus $1$ as the value of $x$ is closer to $1$ by using the L’Hospital’s rule.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Jan 15, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

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 math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved