Discuss the continuity of fx in -0-2- f x - - cos- x - x- 1 - 2x-3 - - x-2 - x- 1 - where - t - represents the greatest integer function- Number of points at which it is discontinuous is

f ( x )={1 amp;x=0 0 nbsp; nbsp; amp;0 lt; x≤ 1/2 1 nbsp; nbsp; amp;1/2 lt; x≤ 1 1× ( 2x 3 )=2x 3 nbsp; nbsp; ...

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Continuity at a Boundary

Discuss the c...

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Discuss the continuity of f(x) in [0,2] $f (x) = {\begin{matrix} [cos π x], & x \leq 1 | 2 x - 3 | [x - 2], & x > 1 \end{matrix}$ where $[t]$ represents the greatest integer function. Number of points at which it is discontinuous is

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f (x) = {\begin{matrix} [c o s π x], & 0 \leq x \leq 1 | 2 x - 3 | [x - 2], & 1 < x \leq 2 \end{matrix}

[.]

f (x) = {\begin{matrix} [cos π x], & 0 \leq x \leq 1 | x - 1 | [x - 2], & 1 < x \leq 2 \end{matrix}

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 1 + [cos \frac{π x}{2}], & 1 < x \leq 2 1 - {x}, & 0 \leq x < 1 | sin π x |, & - 1 \leq x < 0 \end{matrix}

f (1) = 0

f (x) = [x] cos [\frac{2 x - 1}{2}] π

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} [x], & - 2 \leq x \leq - \frac{1}{2} 2 x^{2} - 1, & - \frac{1}{2} < x \leq 2 \end{matrix};

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f (x)

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