If a function f defined by f(x)={\\begin{array}{c}\\\{k ...

CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 25

Total: 50

If a function f defined by
f(x)={

‌

k‌cos‌x

π−2x

,

‌ if ‌x≠‌

π

2

3,

‌ if ‌x=‌

π

2

.
is continuous at x=‌

π

2

, then the value of k is

2
3
6
-6

Solution: 👈: Video 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

‌

k‌cos‌x

π−2x

=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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