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Q.

The value of p and q for which the function f(x)={sin(p+1)x+sinxx , x<0 q , x=0x+x2−xx3/2 , 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

limx→0-sin(p+1)x+sinxx=q=limx→0+x+x2−xx3/2 limx→0-(p+1)cos(p+1)x+cosx=q=12⇒p+1+1=12⇒p=−32; q=12
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