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  4. Find the limit of displaystyle lim x arrow 7+ (|x-7|/x-7)

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Q. Find the limit of $\displaystyle\lim _{x \rightarrow 7^{+}} \frac{|x-7|}{x-7}$

Limits

Solution:

When $x >7,|x-7|=x-7$
$\therefore \displaystyle\lim _{x \rightarrow 7^{+}} \frac{|x-7|}{x-7}=\frac{x-7}{x-7}=1$