The limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$[/tex].
In Mathematics, a limit exists described as a value that a function approaches the output for the provided input values. Limits exist necessary in calculus and mathematical analysis and exist utilized to determine integrals, derivatives, and continuity.
Given:
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)$[/tex]
Substitute the value x = 0, then we get
[tex]$=\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}$[/tex]
Simplify the above equation, we get
[tex]$\frac{0 \cdot \cos (\theta)-\theta \cos (0)}{0-\theta}= 1$[/tex]
Therefore, the limit of
[tex]$\lim _{x \rightarrow 0}\left(\frac{x \cos (\theta)-\theta \cos (x)}{x-\theta}\right)=1$[/tex]
To learn more about limits refer to:
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