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The value of p and q for which the funct...

The value of p and q for which the function `f(x)""={(sin(p+1)x+sinx)/x , x<0q , x=0(sqrt(x+x^2)-sqrt(x))/(x^(3//2)), x >0}` is continuous for all x in R, are: (1) `p=1/2, q=-3/2` (2) `p=5/2, q=-1/2` (3) `p=-3/2, q=1/2` (4) `p=1/2, q=3/2`

Text Solution

Verified by Experts

The correct Answer is:
3
`lim_(n to0)f(0-h) =1+(p+1)=p+2`
`lim_(n to 0) f(0+h) =1/2`
`f(0)=q`
`p+2 =q` and `q=1/2`
`(-3/2, 1/2)`
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Knowledge Check

  • The vertices of triangle are A(-5,3),B(p-1) and C(6,q). If the centroid of the DeltaABC is (1,-1) , then the values of p and q are (i) p=-2,q=5 (ii) p=2,q=-5 (iii) p=3,q=5 (iv) p=-5,q=2

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