The value of p and q for which the function $$f(x)={$$$$sin$$$$(p+1)x+sinxx$$ , x $$0$$ is continuous for all x in R, is

Correct option is 2p=−32, q=12

Questions

The value of p and q for which the function
$f (x) = {\begin{matrix} \frac{\sin (p + 1) x + \sin x}{x}, x < 0 \\ q, x = 0 \\ \frac{\sqrt{x + x^{2}} - \sqrt{x}}{x^{3 / 2}}, x > 0 \end{matrix}$ is continuous for all x in R, is

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p=52, q=12

p=−32, q=12

p=12, q=32

p=12, q=−32

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detailed solution

Correct option is B

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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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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Ready to Test Your Skills?

free study material

The value of p and q for which the function
$f (x) = {\begin{matrix} \frac{\sin (p + 1) x + \sin x}{x}, x < 0 \\ q, x = 0 \\ \frac{\sqrt{x + x^{2}} - \sqrt{x}}{x^{3 / 2}}, x > 0 \end{matrix}$ is continuous for all x in R, is