NIMCET 2016 Question Paper with solutions

Question : 77 of 120

Marks: +1, -0

Consider the function

‘ f ’

defined by

f(x)=\{\table x^2-1\text " ,", x < 3;2ax\text "," , x ≥ 3

for all real numbers

x

. If f is continuous at x=3, then value

a

is;

Solution:

Given that

f(x)=\{\table x^2-1\text " ,", x < 3;2ax\text "," , x ≥ 3

Since, f(x) is continuous at

x=3

then

f(3)=\lim↙{h→0}f(3+h)=\lim↙{h→0}f(3-h)

⇒\lim↙{h→0}2a(3+h)=\lim↙{h→0}[(3-h)^{2}-1]

⇒\lim↙{h→0}(6a+2ah)=\lim↙{h→0}[9+h^{2}-6h-1]

⇒\lim↙{h→0}(6a+2ah)=\lim↙{h→0}[{8+h^{2}-6h]

⇒6a=8

⇒a=\;\;{8}/{6}=\;\;{4}/{3}

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