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JEE Main 2019 · 10 Apr · Shift II

JEE Main 2019 Mathematics question on Limits Continuity and Differentiability

If f(x)={sin⁡(p+1)x+sin⁡xx,x<0q,x=0x+x2−xx3/2,x>0f(x) = \begin{cases} \dfrac{\sin(p+1)x + \sin x}{x}, & x < 0 \\ q, & x = 0 \\ \dfrac{\sqrt{x + x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}

is continuous at x=0x = 0, then the ordered pair (p,q)(p, q) is equal to
  1. A.
    (−32,−12)\left(-\dfrac{3}{2}, -\dfrac{1}{2}\right)
  2. B.
    (−12,32)\left(-\dfrac{1}{2}, \dfrac{3}{2}\right)
  3. C.
    (52,12)\left(\dfrac{5}{2}, \dfrac{1}{2}\right)
  4. D.
    (−32,12)\left(-\dfrac{3}{2}, \dfrac{1}{2}\right)
Show answer

Correct option: D

[JEE Main 2019 · 10 Apr · Shift II]

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