The function defined by fx - x-sin1x for x - 0 0 for x - 0- at x - 0 is

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Continuity of a Function

The function ...

Question

The function defined by
$f (x) = ⎧ ⎨ ⎩ \begin{matrix} x . sin \frac{1}{x} & f o r x \neq 0 0 & f o r x = 0 \end{matrix}$ at $x = 0$ is

continuous

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richt continuous

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left continuous

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can not be determined

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Solution

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Similar questions

f (x)

x = 0

k

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - cos 2 x}{2 x^{2}}, & x < 0 k, & x = 0 \frac{x}{| x |}, & x > 0 \end{matrix}

f (x)

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \begin{matrix} 3, & x = 0 \end{matrix} \begin{matrix} {(1 + \frac{a x + b x^{3}}{x^{2}})}^{1 / x}, & x > 0 \end{matrix} \end{matrix}

x = 0

f : R \to R

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} α + \frac{sin [x]}{x} & i f x > 0 2 & i f x = 0 β + [\frac{sin x - x}{x^{3}}] & i f x < 0 \end{matrix}

[x]

x = 0

β - α =

f (x) = \{\begin{cases} \frac{3 x}{|x| + 2 x}, & x \neq 0 \\ 0, & x = 0 \end{cases} .

\lim_{x \to 0} f (x)

f

f (x) = \frac{x - | x |}{x}

x \neq 0

f (0) = 2

f

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