First slide

Continuity

Question

The value of k so that the function $f (x) = {\begin{matrix} \frac{k \cos x}{π - 2 x} & x \neq \frac{π}{2} \\ 3, & x = \frac{π}{2} \end{matrix}$ is continuous at $x = \frac{π}{2}$ is

Very Easy

A

2
B

4
C

6
D

8

Solution

$f (\frac{π}{2}) = \lim_{x \to \frac{π}{2}} \frac{k \cos 2 x}{π - 2 x} (\frac{0}{0} f o r m b y L' H o s p i t a l r u l e) 3 = \lim_{x \to \frac{π}{2}} \frac{- k \sin 2 x}{- 2} = \frac{k}{2} \Rightarrow k = 6$

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