MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Substitution Method to Remove Indeterminate Form

Let f x = [...

Question

Let $f (x) = \begin{matrix} \frac{k cos x}{π - 2 x} & w h e n x \neq \frac{π}{2} 3 & x = \frac{π}{2} \end{matrix}$ and if $lim x \to \frac{π}{2} f (x) = f (\frac{π}{2})$ .
find the value of`k.

Open in App

Solution

$f (x) = \frac{k cos x}{π - 2 x}$ , when $x \neq \frac{π}{2}$
$= 3$ when $x = \frac{π}{2}$

Now $l i m x \to \frac{π}{2} f (x) = 3$

$\Rightarrow l i m x \to \frac{π}{2} f (x) = \frac{K cos x}{π - 2 x} = 3$

Now $l i m x \to \frac{π}{2} f (x) | \frac{0}{0}$ from

$l i m x \to \frac{π}{2} f (x) |$ Applying L' Hospitalize Rule

$= \frac{- K}{- 2} = \frac{K}{2}$

$∴ \frac{K}{2} = 3$

$\Rightarrow K = 6$

$∴ K = 6$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find the value of

k

is continuous at

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}

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}

\int_{0}^{π / 2} \frac{f (x)}{f (x) + f (\frac{π}{2} - x)} d x,

\int f (x) \neq - f (\frac{π}{2} - x); f o r

0 \leq x \leq \frac{π}{2}

f (x) =

\frac{k cos x}{π - 2 x}

x \neq \frac{π}{2}

3

x = \frac{π}{2}

is continuous at

x = \frac{π}{2}

k

If $f (x) = 0$ is a quadratic equation such that $f (- π) = f (π) = 0$ and $f (\frac{π}{2}) = - \frac{3 π^{2}}{4}$ , then ${lim}_{x \to - π} \frac{f (x)}{sin (sin x)}$ is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Substitution Method to Remove Indeterminate Form

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Substitution Method to Remove Indeterminate Form

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon