`f(x)=("lim")_(n->oo)x/(x^(2n)+1)dotT h e n ,` A. `f(1^+)+f(1^(-1))=0` B. `f(1^+)+f(1^-)+f(1)=3/2` C. `f(-1^+)+f(-1^-)=-1` D. `f(1^+)+f(-1^-)=0`

If f(x)=|(log)_(2)x|, then f(1^(+))=1 (b) f(1^(-))=-1f(1)=1( c) f'(1)=-1

Let f(x)=lim_(n rarr oo)(cos x)/((1+tan^(-1)x)^(n)), then int_(0)^(oo)f(x)dx=

If f(x)=|(log)_(e)x|, then (a) f'(1^(+))=1 (b) f'(1^(-))=-1( c) f'(1)=1(d)f'(1)=-1

If f(x)=lim_(n->oo) {2x+4x^3+...+2n x^(2n-1)}, 0 < x< 1 and int f(x) dx = F(x) and F(1/sqrt(2)) = 2, then (i) F(0)=1, (ii) F(1/2)=4/3, (iii) F(0)=-1, (iv) F(-1/2)=4/3

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1) then for x>0,y>0,f(xy) is equal to

f'(x^(2))=(ln x)/(x^(2)) and f(1)=-(1)/(4), then (A)f(e)=0(B)f'(e)=(1)/(20)

f(x)=(x)/(x-1) then (f(a))/(f(a+1)) is equal to a.f(-a) b.f(1/a) c.f(a^(2)) d.f (-(a)/(a-1))

If f(x)=lim_(n rarr oo)n(x^((1)/(n))-1), then f or x>0,y>0,f(xy) is equal to : f(x)f(y) (b) f(x)+f(y)f(x)-f(y)(d) none of these

If f(x)={[-3x+2,x =1]} ,then which of the following is not true (A) f'(1^(+))=1 (B) f'(1^(-))=-3 (C) f'(1^(-))=f'(1^(+))=1 (D) f is not differentiable at x=1