Answer to Question #186335 in Analytic Geometry for M.Abdullah

Question

Use Numerical Method to find Limit of function    Find  Where n is your arid number for example if your arid number is 19-arid-12345 then choose n=12345. Choose at least 4 most nearest values of n for both (Don’t choose far values from n marks will be deducted in that case). Construct neat table and also perform all calculations. And check whether the limit exist or not? If yes then what’s the value of limit. 

Answer 1

As function is not given , we will consider a function

for understanding purpose

let $f(x) = \frac{sin(x)}{x}$

limit exists for this function

at x $\rightarrow 0$

$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c} \hline x & {\frac{sin(x)}{x}} & x & {\frac{sin(x)}{x}}\\ \hline -0.1 & 0.998334166468 & 0.1&0.998334166468 \\ \hline −0.01 & 0.999983333417 & 0.01 &0.999983333417 \\ \hline -.001 &0.999999833333 & 0.001 & 0.999999833333 \\ \hline -.0001 & 0.999999998333 & 0.0001&0.999999998333 \\ \hline \end{array}$

Table of Functional Values for $\frac{sin(x)}{x}$

The values in this table were obtained using a calculator and using all the places given in the calculator output.

As we read down each $\frac{sin(x)}{x}$    column, we see that the values in each column appear to be approaching one. Thus, it is fairly reasonable to conclude that $\underset{x\to 0}{\lim}\frac{\sin x}{x}=1$  . A calculator-or computer-generated graph of $f(x)=\frac{\sin x}{x}$  would be similar to that shown in (Figure), and it confirms our estimate.