Pls answer this: Pls answer this: A. B. c. D. .f(x) Column—I = x2 sin(l//x), f (0) = 0 4 = xsin yx,f (0) = 0 = x 3 sin h, f (0) = 0 p. q. 2 9 S. Column-II continuous not derivable f is differentiable everywhere but f' not continuous is not continue ' f ' is continuous but not derivable Share with your friends Share 0 Ghanshyam Dhakar answered this Dear student, A . fx = x2sin1x ,f0=0RHL =limx→0+fx = limx→0+x2sin1x = 0LHL =limx→0-fx = limx→0-x2sin1x = 0RHL = LHL =f0 ⇒ fx is continuous RHD =limh→0 fx+h-fx h = limh→0 0+h2sin10+h-0h =0LHD =limh→0 fx-h-fx -h = limh→0 0-h2sin10-h-0-h = 0f'x =2xsin1x-x2×1x2cos1x=2xsin1x-cos1x limx→02xsin1x-cos1x = 0-cos∞ = constant LHD =RHD≠f'0 ⇒ fx is not differentiable answer sB.fx = x-4x4-x4131-8x314, f12 = 29RHL =limx→12+fx = limx→12+ x-4x4-x4131-8x31400 form so use L' Hospital's RuleRHL =limx→12+fx = limx→12+ 1-16x32x-4x4-13×4x4-23-148x3-34×24x2 = 1-22×12-13×418-23-141-34×24×14 = -1-13-64=4332=89RHL ≠f12 ⇒ fx is not continuousanswer rC . fx = xsin1x ,f0=0RHL =limx→0+fx = limx→0+xsin1x = 0 LHL =limx→0-fx = limx→0-xsin1x = 0RHL = LHL =f0 ⇒ fx is continuous RHD =limh→0 fx+h-fx h = limh→0 0+hsin10+h-0h =constant f' is not continuousanswer qD. fx = x3sin1x ,f0=0RHL =limx→0+fx = limx→0+x3sin1x = 0LHL =limx→0-fx = limx→0-x3sin1x = 0RHL = LHL =f0 ⇒ fx is continuous RHD =limh→0 fx+h-fx h = limh→0 0+h3sin10+h-0h = 0LHD =limh→0 fx-h-fx -h = limh→0 0-h3sin10-h-0-h = 0f'x =3x2sin1x-x3×1x2cos1x=2xsin1x-xcos1xlimx→03x2sin1x-xcos1x = 0 LHD =RHD= f0 ⇒ fx is differentiable ⇒ f'x is continuous RHD =limh→0 f'x+h-f'x h = limh→0 20+hsin10+h-0+hcos10+h-0h = limh→0 2sin10+h-cos10+h-01=constantf'x is not derivable answer s Hope this information will clear your doubts. If you have any more doubts just ask here on the forum and our experts will try to help out as soon as possible. Regards 0 View Full Answer
