Let f(x) = [2x^3 - 5],where [cdot] denotes th | vedclass

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(B) The function $f(x) = [2x^3 - 5]$ is discontinuous at points where the argument $2x^3 - 5$ is an integer. We are looking for points $x \in (1, 2)$

Vedclass · Accepted Answer

$13$

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(B) The function $f(x) = [2x^3 - 5]$ is discontinuous at points where the argument $2x^3 - 5$ is an integer. We are looking for points $x \in (1, 2)$ such that $2x^3 - 5 = k$,where $k$ is an integer. Since $x \in (1, 2)$,we have $1 Cubing the inequality,we get $1 Multiplying by $2$,we get $2 Subtracting $5$,we get $2 - 5 Thus,the possible integer values for $k$ are $\{-2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. There are $13$ such integer values. For each integer $k$,there exists a unique $x = \sqrt[3]{\frac{k+5}{2}}$ in the interval $(1, 2)$. Therefore,there are $13$ points of discontinuity in the interval $(1, 2)$.

Let $f(x) = [2x^3 - 5]$,where $[\cdot]$ denotes the Greatest Integer Function. Find the number of points in the interval $(1, 2)$ where the function $f(x)$ is discontinuous.

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