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Q.

The function fx is defined as below fx=sin(a+1)x+sin2x2x,           if  x<0b                   ,           if x =0x+bx3−xbx52,                     if x>0   If the function fx is continuous at x=0 then the value of a+b is

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a

−52

b

-3

c

-2

d

−32

answer is D.

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Detailed Solution

Given that the function fx  is continuous at x=0⇒limx→0−sin(a+1)x+sin2x2x=limx→0+x+bx3−xbx52=f0⇒a+12+1=limx→0+x1+bx2−1bxx2=b⇒a+32=limx→0+1+bx2−1bx21+bx2+11+bx2+1=b⇒a+32=limx→0+bx2bx211+bx2+1=b⇒a+32=12=b⇒b=12,a=−2⇒a+b=−32
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The function fx is defined as below fx=sin(a+1)x+sin2x2x,           if  x<0b                   ,           if x =0x+bx3−xbx52,                     if x>0   If the function fx is continuous at x=0 then the value of a+b is