let `f(x)=2+cosx` for all real x Statement 1: For each real t, there exists a pointc in `[t,t+pi]` such that `f'(c)=0` Because statement 2: `f(t)=f(t+2pi)` for each real t

let f(x)=2+cos x for all real x Statement 1: For each real t,there exists a pointc in [t,t+pi] such that f'(c)=0 Because statement 2:f(t)=f(t+2 pi) for each real t

let f(x)=2+cosx for all real x. Statement 1: For each real t, there exists a point c in [t,t+pi] such that f '(c)=0 . Statement 2: f(t)=f(t+2pi) for each real t

Statement I For each eal, there exists a pooint c in [t,t+pi] such that f('c) Because Statement II f(t)=f(t+2pi) for each real t .

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Consider the statements: P: There exists some x in IR such that f(x)+2x=2(1+x^(2)) Q: There exists some x in IR such that 2f(x)+1=2x(1+x) Then

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Consider the statements : P : there exists some x in RR such that f(x)+2x=2(1+x^(2)) Q : There exists some x in RR such that 2f(x)+1=2x(1+x) then-

If f(x)=x^(2)+bx+c and f(2+t)=f(2-t) for all real number t, then which of the following is true?

Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and lim_(t->x) (t^2f(x)-x^2f(t))/(t-x)=1 for each x>0 . Then f(x)=

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(2)(x+pi)=sin^(2)x for all real x.

Let F(x) be an indefinite integral of sin^(2)x Statement I The function F(x) satisfies F(x+pi)=F(x) for all real x. Because Statement II sin^(2)(x+pi)=sin^(2)x, for all real x.

Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and lim_(t rarr x)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each x>0 Then f(x)=