[" (3) Let "[(1)/(2),1]rarr R" (the set of all real numbers) be a positive non-constrant,and differentable "],[" function such that "f(x)-2(x)" and "f(2)=1" .Then the value of "int_(1/2)^(1)f(x)" br hes in the interval "],[[" (4) "(2x-1,2)," (3) "(x-1,2x-1)]]

Let f:[(1)/(2),1]to RR (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x)lt2f(x)" and "f((1)/(2))=1 Then the value of int_((1)/(2))^(1)f(x)dx lies in the interval

Let f:[(1)/(2),1]rarr R (the set of all real numbers) be a positive,non-constant,and differentiable function such that f'(x)<2f(x) and f((1)/(2))=1. Then the value of int_((1)/(2))^(1)f(x)dx lies in the interval (a) (2e-1,2e)(b)(3-1,2e-1)(c)((e-1)/(2),e-1)( d) (0,(e-1)/(2))

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x) and f(1/2)=1 . Then the value of int f(x)dx lies in the interval for x:[1/2,1] (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

Let f: R rarr R be a function such that f(2)=4 and f'(2)=1 . Then, the value of lim_(x rarr 2) (x^(2)f(2)-4f(x))/(x-2) is equal to