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Question

The function is defined by f(x) ={Kx=1, if x53x5, if x>5 at x = 5.

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Solution

Here, f(x) ={Kx+1, if x53x5, if x>5

LHL = limx5f(x)=limx5λ(kx+1)

Putting x=5-h as x5 when h0
limh0=[k(5h)+1]limh0[5kkh+1]=5k+1

RHL = limx5+f(x)=limx5+λ(kx+1)

Putting x=5-h as x5+ when h0

limh0=[3(5h)5]limh0[10+3h]=10

Also, f(x)=5k+1 [ f(x)=kx+1]

Since, f(x) is continuous at x = 5.

LHL=RHL=f(5)5k+1=10k=95


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