If `f(x)=lim_(n->oo)(2sinx)^n` for all `x in [0,pi/6]` , Then which of following statements is true (A)`f(pi/6)` not equal to 1(B) `f(x)` has irremovable discontinuity at `x=pi/6` (c) `f(x)` has removable discontinuity at `x=pi/6` (D) `f(x)` is coninuous in `(0,pi/6)`

If f(x)={(2cos x-sin2x)/((pi-2x)^(2)),x (pi)/(2) then which of the following holds? (a)f is continuous at x=pi/2( b) f has an irremovable discontinuity at x=pi/2( d) f has a removable discontinuity at x=pi/2( d) None of these

Let f(x)=sin[pi/6sin(pi/2sinx)] for all x in RR

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

If f(x)={(2cos x -sin2x)/((pi-2x)^2),xlt=pi/2(e^(-cotx)-1)/(8x-4pi),x >pi/2 , then which of the following holds? (a) f is continuous at x=pi//2 (b) f has an irremovable discontinuity at x=pi//2 (c) f has a removable discontinuity at x=pi//2 (d)None of these

If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a))])/(a-x) for x < a, then a. f(a^-)<0 b. f has a removable discontinuity at x=a c. f has an irremovable discontinuity at x=a d. f(a^+)<0

If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a))])/(a-x) for x < a, then a. f(a^-)<0 b. f has a removable discontinuity at x=a c. f has an irremovable discontinuity at x=a d. f(a^+)<0

If f(x)={sin((a-x)/2)t a n[(pix)/(2a)] for x > a and ([cos((pix)/(2a))])/(a-x) for x < a, then f(a^-)<0 b. f has a removable discontinuity at x=a c. f has an irremovable discontinuity at x=a d. f(a^+)<0

If f(x)={sin((a-x)/(2))tan[(pi x)/(2a)] for x>a and ([cos((pi x)/(2a))])/(a-x) for x

f(x)= (1-sinx+cosx)/(1+sinx+cosx) discontinuous at x=pi . Find f(pi) so that f(x) is continuous x=pi

Let f:(0, pi)->R be a twice differentiable function such that (lim)_(t->x)(f(x)sint-f(x)sinx)/(t-x)=sin^2x for all x in (0, pi) . If f(pi/6)=-pi/(12) , then which of the following statement(s) is (are) TRUE? f(pi/4)=pi/(4sqrt(2)) (b) f(x)<(x^4)/6-x^2 for all x in (0, pi) (c) There exists alpha in (0, pi) such that f^(prime)(alpha)=0 (d) f"(pi/2)+f(pi/2)=0