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

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) 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^(3)(x+pi)=sin^(2)x for all real x. A) Statement-1: True , statement-2 is true, Statement -2 is not a correct explanation for statement -1 c) Statement-1 is True, Statement -2 is False. D) Statement-1 is False, Statement-2 is True.

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

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 rarr x)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each x>0 Then f(x)=

If f(x) is an integrable function over every interval on the real line such that f(t+x)=f(x) for every x and real t, then int_(a)^(a+1) f(x)dx is equal to