CBSE Class 12 Math 2022 Term I Solved Paper - Question 25 | ...

CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 25 of 50

Marks: +1, -0

If a function

f

defined by

f(x)={\{\table \;{k \cos x}/{π-2 x} {,}, \;\text " if "\; x ≠ \;{π}/{2} ; 3{,} , \;\text " if "\; x=\;{π}/{2} }.

is continuous at

x=\;{π}/{2}

, then the value of

k

is

2
3
6
-6

Solution:

Explanation: Since,

f(x)

is continuous at

x=\;{π}/{2}

Therefore,

\;\; \lim ↙{x → \;{π}/{2}} f(x)=f (\;{π}/{2})

⇒ \;\; \lim ↙{x → \;{π}/{2}} \;{k \cos x}/{π-2 x}=3

⇒ \;\; k \lim ↙{x → \;{π}/{2}} \;{ sin \; ({π}/{2}-x) }/{2 (\;{π}/{2}-x) }=3

⇒ \;\; \;{k}/{2} \lim ↙{x → \;{π}/{2}} \;{ sin \; ({π}/{2}-x) }/{ (\;{π}/{2}-x) }=3

⇒ \;\; \;{k}/{2} × 1=3 ⇒ k=6

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