The value of k for which fx - - sin x - xcos x-x3cos x- x 0- k- x - 0 - is continuous at x - 0- isk - - - - - fx - - sin x - xcos x-x3cos x- x 0- k- x - 0 - x - 0 - - -

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Continuity of a Function

The value of ...

Question

The value of k for which $f (x) = {\begin{matrix} \frac{sin x - x cos x}{x^{3} cos x}, & x \neq 0 k, & x = 0 \end{matrix}$ is continuous at x = 0, is

k के किस मान के लिए, $f (x) = {\begin{matrix} \frac{sin x - x cos x}{x^{3} cos x}, & x \neq 0 k, & x = 0 \end{matrix}$ , x = 0 पर सतत है?

\frac{1}{2}

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\frac{- 1}{6}

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\frac{1}{6}

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\frac{1}{3}

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{\begin{matrix} \frac{1 - cos 3 x}{x^{2}}, & i f x \neq 0 K, & i f x = 0 \end{matrix}

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f (x)

x = 0

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{e^{\frac{1}{x}}}{1 + e^{\frac{1}{x}}} x \neq 0 0 x = 0 \end{matrix}

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