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Question

The function f(x)=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪x2/a,0x<1a,1x<22b24bx2,2x< is continuous for 0x<, then the most suitable values of a and b are

A
a=1,b=1
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B
a=1,b=1+2
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C
a=1,b=1
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D
None of these
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Solution

The correct option is C a=1,b=1
Since, f is continuous for 0x<,f is continuous at x=1.

limx1x2a=a

a=±1

Since, f is continuous at x=2.

limx22b24bx2=a

2b24b2=a

b22b=a

When a=1,b22b=1

b=1±2

When a=1,b22b=1

(b1)2=0b=1

Hence, a=1 and b=1 are most suitable values.

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