If `x=f''(t) cos t + f' (t) sin t , y =-f'' (t) sin t + f' (t) cos t`,then `int[((dx)/(dt))^2+((dy)/(dt))^2]^(1/2) dt ` is equal to

If x=f(t )cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2

cos t dx/dt + sin t = 1

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= f(t)-f"(t) (b) {f(t)-f"(t)}^2 (c) {f(t)+f"(t)}^2 (d) none of these

If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ((dx)/(dt))^2+((dy)/(dt))^2= f(t)-f"(t) (b) {f(t)-f"(t)}^2 (c) {f(t)+f"(t)}^2 (d) none of these

If x= f(t )cost-f^(prime)(t)sinta n dy=f(t)sint+f^(prime)(t)cost ,t h e n((dx)/(dt))^2+((dy)/(dt))^2 (a) f(t)-f^(primeprime)(t) (b) {f(t)-f^(primeprime)(t)}^2 (c) {f(t)+f^(primeprime)(t)}^2 (d) none of these

f(x) = int_(x)^(x^(2))(e^(t))/(t)dt , then f'(t) is equal to :

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to

lim_(x to 0)(int_(-x)^(x) f(t)dt)/(int_(0)^(2x) f(t+4)dt) is equal to