If f ( x ) = { k cos x - 2 x , x 2 3 , x = 2 is continuous at x = 2 , then k is:

Question

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

Smart Achievers · Accepted Answer

(1)

Ans. 6

Explanation:

If $f (x)$ is continuous at $x = \frac{π}{2}$

Then, $\frac{k \cos x}{π - 2 x} = 3$

$\Rightarrow$ $x = \frac{π}{2},$

Using L' Hospital rule,

$\frac{k (- \sin (\frac{π}{2}))}{- 2} = 3$

$\Rightarrow$ $\frac{k}{2} = 3$

$\Rightarrow$ $k = 6$

Solution

Q.
If $f (x) =$ ${\begin{matrix} \frac{k \cos x}{π - 2 x}, & x \neq \frac{π}{2} \\ 3, & x = \frac{π}{2} \end{matrix}$ is continuous at $x = \frac{π}{2},$ then $k$ is:

1 6

2 4

3 3

4 2

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Solution

Q. If f(x)={kcosxπ-2x,x≠π23,x=π2 is continuous at x=π2, then k is:

1 6

2 4

3 3

4 2

Ans. (1) Ans. 6 Explanation: If f(x) is continuous at x=π2 Then, kcosxπ-2x=3 ⇒ kcos(π2)π-2(π2)=3 Using L' Hospital rule, k(-sin(π2))-2=3 ⇒ k2=3 ⇒ k=6

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Q.
If $f (x) =$ ${\begin{matrix} \frac{k \cos x}{π - 2 x}, & x \neq \frac{π}{2} \\ 3, & x = \frac{π}{2} \end{matrix}$ is continuous at $x = \frac{π}{2},$ then $k$ is: