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=` (a)`f(t)-f^(primeprime)(t)` (b) `{f(t)-f^(primeprime)(t)}^2` (c) `{f(t)+f^(primeprime)(t)}^2` (d) none of these

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

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

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 =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) and y=phi (t) then to prove that (dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(phi'(t))/(f'(t)) .

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a) f^(primeprime)(x)=f(x)=0 (b) 4f^(primeprime)(x)+f(x)=0 (c) f^(primeprime)(x)+f(x)=0 (d) 4f^(primeprime)(x)-f(x)=0