If `f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot`

Iff(x)=int_1^x(logt)/(1+t+t^2)dxAAxlt=1,t h e np rov et h a tf(x)=f(1/x)dot

If f(x)=|x^2-5x+6|,t h e nf^(prime)(x)e q u a l s

If x y^2=1,p rov et h a t2(dy)/(dx)+y^3=0

Ify=int_0^xf(t)sin{k(x-t)}dt ,t h e np rov et h a t(d^2y)/(dx^2)+k^2y=kf(x)dot

f: Rvec[-1,oo)a n df(x)=1n([|s in2x|+|cos2x|]) (where [.] is the greatest integer function.) Then, f(x)h a sr a ngZ f(x)i sp e r iod i cw i t hfu n d a m e n t a lp e r iodpi/4 f(x)i sin v e r t i b l ein[0,pi/4] f(x)i sin tofu n c t iondot

With usual notion, if in triangle A B C , (b+c)/(11)=(c+a)/(12)=(a+b)/(13),t h e np rov et h a t (cosA)/7=(cosB)/(19)=(cosC)/(25)

If x^(13)y^7=(x+y)^(20),p rov et h a t(dy)/(dx)=y/xdot

If f(x)=int_0^x tf(t)dt+2, then

If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

If int_0^ycost^2dt=int_0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)