If graph of `y=f(x)` is symmetrical about the y-axis and that of `y=g(x)` is symmetrical about the origin and if `h(x)=f(x)dotg(x),t h e n(d^3h(x))/(dx^3)a tx=0` is (a)cannot be determined (b) `f(0)dotg(0)` (c)0 (d) none of these

The graph of the function y= f (x) is symmetrical about the line x=2 then

If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(7)=3, then the value of f^(prime)(3) is__________

If g(x)=|a^(-x)e^(x log_e a)x^2a^(-3x)e^(3x log_e a)x^4a^(-5x)e^(5x log_e a)1| , then graphs of g(x) is symmetrical about the origin graph of g(x) is symmetrical about the y-axis ((d^4g(x))/(dx^4)|)_(x=0)=0 f(x)=g(x)xxlog((a-x)/(a+x)) is an odd function

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-a xi s ,then n equals 2 (b) 2/3 (c) 1/4 (d) 1/3

If R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) non of these

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If 'f' is an increasing function from RvecR such that f^(x)>0a n df^(-1) exists then (d^2(f^(-1)(x)))/(dx^2) is 0 c. =0 d. cannot be determined

If f(x)=lim_(n->oo)n(x^(1/n)-1),t h e nforx >0,y >0,f(x y) is equal to : (a) f(x)f(y) (b) f(x)+f(y) (c) f(x)-f(y) (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these