(C) Given that $f(x) = [x-3] + |x-4|$.To find $\lim_{x \rightarrow 3^{-}} f(x)$,let $x = 3 - h$,where $h \rightarrow 0$ and $h > 0$.$\lim_{x \rightarr

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(C) Given that $f(x) = [x-3] + |x-4|$.To find $\lim_{x \rightarrow 3^{-}} f(x)$,let $x = 3 - h$,where $h \rightarrow 0$ and $h > 0$.$\lim_{x \rightarrow 3^{-}} f(x) = \lim_{h \rightarrow 0} ([3 - h - 3] + |3 - h - 4|)$$= \lim_{h \rightarrow 0} ([-h] + |-1 - h|)$Since $h$ is a very small positive number,$-h$ is a very small negative number,so $[-h] = -1$.Also,$|-1 - h| = |-(1 + h)| = 1 + h$.Therefore,$\lim_{h \rightarrow 0} (-1 + 1 + h) = 0$.

Class 11 Mathematics Limits Concept of limits, Evaluation of algebric limits

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If $f: R \rightarrow R$ is defined by $f(x) = [x-3] + |x-4|$ for $x \in R$,then $\lim_{x \rightarrow 3^{-}} f(x)$ is equal to

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$-2$
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$-1$
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$0$
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$1$

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Limits

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If $f: R \rightarrow R$ is defined by $f(x) = [x-3] + |x-4|$ for $x \in R$,then $\lim_{x \rightarrow 3^{-}} f(x)$ is equal to

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