JEE Main 201910 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002Iff(x)={sin(p+1)x+sinxx,x<0q,x=0x+x2−xx\raise0.5ex3/\lower0.25ex2,x>0f(x) = \left\{ {\matrix{ {{{\sin (p + 1)x + \sin x} \over x}} & {,x < 0} \cr q & {,x = 0} \cr {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{{\raise0.5ex\hbox{$\scriptstyle 3$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}}}} & {,x > 0} \cr } } \right.f(x)=⎩⎨⎧xsin(p+1)x+sinxqx\raise0.5ex3/\lower0.25ex2x+x2−x,x<0,x=0,x>0 is continuous at x = 0, then the ordered pair (p, q) is equal toAOption A. (−32,−12)\left( { - {3 \over 2}, - {1 \over 2}} \right)(−23,−21)BOption B. (−12,32)\left( { - {1 \over 2},{3 \over 2}} \right)(−21,23)COption C. (−32,12)\left( { - {3 \over 2}, {1 \over 2}} \right)(−23,21)DOption D. (52,12)\left( { {5 \over 2}, {1 \over 2}} \right)(25,21)CheckSkip · show solution
