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Q.

Let  f:RR be defined as  f(x)={λ|x25x+6|μ(5xx26),   x<2etan(x2)x[x]                 ,   x>2μ                             ,    x=2  where [x] is the greatest integer less than or equal to x. if f(x) is continuous at x = 2, then  λμ is equal to:

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a

e (e  2)

b

1

c

2e  1

d

e(e+1)

answer is A.

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Detailed Solution

R.H.L=limx2+f(x)=limx2+etan(x2)x2=e1   [       limx2+[x]=2] L.H.L=limx2f(x)=limx2λ(x2)(x3)μ(x2)(x3)=λμ

Given that  f(x) is continuous at  x=2

                  μ=e=λμ   μ=e,λ=e2

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