If fx- 2 x-2 -16 4 x -16 - if x- 2 k - if x - 2 is continuous at x-2- find k

Consider the following #10;question. #10; #10;Find the value of #8220;k #8221; we get. #10; #10; #160; f(x)=( #10; #10; #160; ...

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Theorems for Continuity

If fx= 2 x+...

Question

If $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{2^{x + 2} - 16}{4^{x} - 16}, i f x \neq 2 k, i f x = 2 \end{matrix}$ is continuous at $x = 2$ , find $k$

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k

f (x)

x = 2.

f (x) = ⎧ ⎨ ⎩ \begin{matrix} 2 x + 1; i f x < 2 k; x = 2 3 x - 1; x > 2 \end{matrix}

k

x = \frac{π}{2}

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{k cos x}{π - 2 x}, if x \neq \frac{π}{2} 3, if x = \frac{π}{2} \end{matrix}

k

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{k cos x}{π - 2 x}, i f x \neq \frac{π}{2} 3, i f x = \frac{π}{2} \end{matrix}

x = \frac{π}{2}

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \frac{2^{x + 2} - 16}{4^{x} - 16}, i f x \neq 2 k, i f x = 2 \end{matrix}

x = 2

K

f (x)

x = \frac{π}{2}

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{K . cos x}{π - 2 x}, i f x \neq \frac{π}{2} 3 i f x = \frac{π}{2} \end{matrix}

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