The greatest value of the function fx-sinx-x-e-x-2-1 for all x-O- is

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Left Hand Limit

The greatest ...

Question

The greatest value of the function $f (x) = sin {x [x] + e^{[x]} + \frac{π}{2} - 1}$ for all $x \in [O, \infty)$ is

-1

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f (x) = \frac{sin x}{[\frac{x}{π}] + \frac{1}{2}}

[x]

f (x)

x = \frac{π}{2}

f (x) = \frac{1 - sin x}{{(\frac{π}{2} - x)}^{2}}

x \neq \frac{π}{2}

= 3

x = \frac{π}{2}

f (x) = \frac{1 - sin x + cos x}{1 + sin x + cos x}

f (π)

f (x)

x = π

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} [\frac{2 (sin x - {sin}^{3} x) + ∣ ∣ sin x - {sin}^{3} x ∣ ∣}{2 (sin x - {sin}^{3} x) - ∣ ∣ sin x - {sin}^{3} x ∣ ∣}], x \neq \frac{π}{2} f o r x \in (0, π) 3 x = \frac{π}{2} \end{matrix}

[]

f (x) = \frac{1 - sin x + cos x}{1 + sin x + cos x}

x = π

f (π)

f (x)

x = π

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