JEE Main 2011Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002The value of ppp and qqq for which the function f(x)={sin(p+1)x+sinxx,x<0q,x=0x+x2−xx3/2,x>0f\left( x \right) = \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^{3/2}}}}} & {,x > 0} \cr } } \right.f(x)=⎩⎨⎧xsin(p+1)x+sinxqx3/2x+x2−x,x<0,x=0,x>0 is continuous for all xxx in R, areAOption A. p=p =p= 52{5 \over 2}25, q=q =q= 12{1 \over 2}21BOption B. p=p =p= −32-{3 \over 2}−23, q=q =q= 12{1 \over 2}21COption C. p=p =p= 12{1 \over 2}21, q=q =q= 32{3 \over 2}23DOption D. p=p =p= 12{1 \over 2}21, q=q =q= −32-{3 \over 2}−23CheckSkip · show solution
