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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`

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To determine the values of \( p \) and \( q \) for which the function \[ f(x) = \begin{cases} \frac{\sin(p+1)x + \sin x}{x} & \text{if } x < 0 \\ q & \text{if } x = 0 \\ \frac{\sqrt{x + x^2} - \sqrt{x}}{x^{3/2}} & \text{if } x > 0 ...
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