For what value of k- is the function fx- k cos x-2 x- if x-2- 3 if x-2 - continuous for all real x -A- 0B- TC- 3D -6

The correct option is D 6Since f(x) is continuous at x=π2 ∴ f(π2)=lim_x→π/2 f(x)=lim_x→π/2kcos xπ 2x →00 Apply L'hospital lim_x→π/2 ksin x 2=3 ⇒ nbsp;lim ...

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Standard XII

Mathematics

Single Point Continuity

For what valu...

Question

For what value of k, is the function $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{k cos x}{π - 2 x}, if x \neq \frac{π}{2} 3 if x = \frac{π}{2} \end{matrix}$ continuous for all real $x ?$

0

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3

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6

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Solution

The correct option is D $6$
Since $f (x)$ is continuous at $x = \frac{π}{2}$
$∴ f (\frac{π}{2}) = lim x \to \frac{π}{2} f (x) = lim x \to \frac{π}{2} \frac{k cos x}{π - 2 x} \to \frac{0}{0}$
Apply L'hospital
$lim x \to \frac{π}{2} \frac{- k sin x}{- 2} = 3 \Rightarrow lim x \to \frac{π}{2} \frac{k sin x}{2} = \frac{k}{2}$
$\frac{k}{2} = 3 \Rightarrow k = 6$

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Similar questions

Q. Find the value of

k

is continuous at

x = \frac{π}{2}

, where

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}

Q. Determine the value of

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}

is continuous at

x = \frac{π}{2}

Q. Find the value of

K

f (x)

is continuous at

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}

Q. Find the value of

p

and

q

for which

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

is continuous at

x = π / 2

Q. Let

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x i f x \leq - \frac{π}{2} A sin x + B i f - \frac{π}{2} < x < \frac{π}{2}; cos x i f x \geq \frac{π}{2} \end{matrix}

For what values of

A

and

B

, the function

f (x)

is continuous throughout real line?

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For what value of k, is the function f(x)=⎧⎪ ⎪⎨⎪ ⎪⎩kcosxπ−2x, if x≠π2 3 if x=π2 continuous for all real x ?

The correct option is D 6Since f(x) is continuous at x=π2 ∴f(π2)=limx→π2f(x)=limx→π2kcosxπ−2x →00 Apply L'hospital limx→π2−ksinx−2=3⇒limx→π2ksinx2=k2 k2=3⇒k=6

For what value of k, is the function $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{k cos x}{π - 2 x}, if x \neq \frac{π}{2} 3 if x = \frac{π}{2} \end{matrix}$ continuous for all real $x ?$