(B) We are given the function $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}$.To find $\lim_{x \rightarrow 0^

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(B) We are given the function $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & [x] \neq 0 \\ 0, & [x] = 0 \end{cases}$.To find $\lim_{x \rightarrow 0^{-}} f(x)$,we consider values of $x$ slightly less than $0$.For $x \in (-1, 0)$,the greatest integer function $[x] = -1$.Therefore,$\lim_{x \rightarrow 0^{-}} f(x) = \lim_{x \rightarrow 0^{-}} \frac{\sin(1+[x])}{[x]}$.Substituting $[x] = -1$,we get $\frac{\sin(1-1)}{-1} = \frac{\sin(0)}{-1} = \frac{0}{-1} = 0$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

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

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If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

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Which of the following plants exhibits a haplontic life cycle?

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