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Theorems for Continuity

If f( x ...

Question

If $f (x) = {\begin{matrix} \frac{sin (cos x) - cos x}{{(π - 2 x)}^{3}}, i f k \end{matrix} \begin{matrix} x \neq \frac{π}{2}, i f x = \frac{π}{2} \end{matrix}$ is continuous at $x = \frac{π}{2}$ , then $k =$

0

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- \frac{1}{2}

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- \frac{1}{24}

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- \frac{1}{48}

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f (x)

\frac{sin (cos x) - cos x}{(π - 2 x)^{3}}

x \neq

\frac{π}{2} k

x = \frac{π}{2}

x = \frac{π}{2}

k

f (x) = \frac{s i n (c o s x) - c o s x}{(π - 2 x)^{3}}, i f x \neq \frac{π}{2} = k, i f x = \frac{π}{2}

continuous at x = \frac{π}{2}, then k =

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, if x < \frac{π}{2} a, if x = \frac{π}{2} \frac{b (1 - sin x)}{(π - 2 x)^{2}}, if x > \frac{π}{2} \end{matrix}

f (x)

x = \frac{π}{2}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, i f x < \frac{x}{2} p, i f x = \frac{π}{2} \frac{q (1 - sin x)}{(π - 2 x)^{2}}, i f x > \frac{π}{2} \end{matrix}

x = \frac{π}{2}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1 - {sin}^{3} x}{3 {cos}^{2} x}, i f x < \frac{π}{2} a, i f x = \frac{π}{2} \frac{b (1 - sin x)}{{(π - 2 x)}^{2}}, i f x > \frac{π}{2} \end{matrix}

f (x)

x = \frac{π}{2}

a

b

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