NIMCET 2012 Question Paper with solutions

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Question : 23 of 120

Marks: +1, -0

What is the value of a for which f (x) =

\{\table sinx , \if x ≤ π/2;ax,\if x > π/2

is continuous ?

π
$π/2$
$2/π$
0

Solution:

function is continuous at

π/2

∴

\lim↙{x→π/2}

f (x) = f

(π/2)

⇒

\lim↙{x→π/2}

f (x) = f

(π/2)

⇒

\lim↙{h→0}

a

(h+π/2)

= sin

π/2

⇒ a

(0+π/2)

= 1
∴ a =

2/π

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