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Q.

If  fx=acosx-cosbxx2,  x≠0  and f0=4 is continuous at  x=0, then the ordered pair (a, b) is

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a

±1,  3

b

1,  ±3

c

-1,-3

d

1,  3

answer is B.

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Detailed Solution

We  must  have   limx→0  acosx-cosbxx2=4or             limx→0a1-x22!-1-b2x22!x2=4or             limx→0  a-1x2-a2-b22=4or             a=1  and  a2-b22=-4or             a=1  and  b2=9or             a=1  and  b=±3
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If  fx=acosx-cosbxx2,  x≠0  and f0=4 is continuous at  x=0, then the ordered pair (a, b) is