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Modulus Function

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Question

Find the values of k so that the function f is continuous at the indicated point.

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Solution

The given function is

The given function f is continuous at x = 2, if f is defined at x = 2 and if the value of f at x = 2 equals the limit of f at x = 2

It is evident that f is defined at x = 2 and

Therefore, the required value of.

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Similar questions

k

f

f (x) =

{\begin{matrix} k x^{2}, i f x \leq 2 3, i f x > 2 \end{matrix}

x = 2

k

f

f (x) =

{\begin{matrix} k x + 1, i f x \leq 5 3 x - 5, i f x > 5 \end{matrix}

x = 5

Find the value of k, so that the function f(x) is continuous at the indicated point

$f (x) = \frac{\sqrt{3} - tan x}{π - 3 x} = k$ at

$x = \frac{π}{3}$

k

f

f (x) =

{\begin{matrix} k x^{2}, if x \leq π cos x, if x > π \end{matrix}

x =

π

k

f

f (x) =

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

x =

\frac{π}{2}

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