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Q.

The values of p and q for which the function f(x)=sin(p+1)x+sinxx,if x < 0q,if x = 0x+x2−xx32,if x > 0   is continuous for all x in R, is

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a

p=52,q=12

b

p=-32,q=12

c

p=12,q=32

d

p=12,q=-32

answer is B.

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Detailed Solution

L H L limx→0 sinp+1xp+1xp+1+sinxx=p+1+1=p+2R HLlimx→0 x x+1-1 xx=limx→0 x+1-1xx+1+1=1/2LHL=RHL=f(0)
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The values of p and q for which the function f(x)=sin(p+1)x+sinxx,if x < 0q,if x = 0x+x2−xx32,if x > 0   is continuous for all x in R, is