The value of `int_1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,w h e r ea >1,a n d[x]` denotes the greatest integer not exceeding `x ,` is `af(a)-{f(1)f(2)++f([a])}` `[a]f(a)-{f(1)+f(2)++f([a])}` `[a]f(a)-{f(1)+f(2)++fA}` `af([a])-{f(1)+f(2)++fA}`

The value of int_1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,where a >1, and [x] denotes the greatest integer not exceeding x, is (A) af(a)-{f(1)f(2)+.....+f([a])} (B) [a]f(a)-{f(1)+f(2)+......+f([a])} (C) [a]f(a)-{f(1)+f(2)+.......+fA} (D) af([a])-{f(1)+f(2)+......+fA}

The value of int_1^a[x]f^(prime)(x)dxf^(prime)(x)dx ,where a >1 , and [x] denotes the greatest integer not exceeding x, is (A) af(a)-{f(1)f(2)+.....+f([a])} (B) [a]f(a)-{f(1)+f(2)+......+f([a])} (C) [a]f(a)-{f(1)+f(2)+.......+fA} (D) af([a])-{f(1)+f(2)+......+fA}

The value of int_1^a[x]f^(prime)(x)dx ,where a >1 , and [x] denotes the greatest integer not exceeding x, is (A) af(a)-{f(1)f(2)+.....+f([a])} (B) [a]f(a)-{f(1)+f(2)+......+f([a])} (C) [a]f(a)-{f(1)+f(2)+.......+fA} (D) af([a])-{f(1)+f(2)+......+fA}

The value of int_1^a[x]f^(prime)(x)dx ,where a >1 , and [x] denotes the greatest integer not exceeding x, is (A) af(a)-{f(1)f(2)+.....+f([a])} (B) [a]f(a)-{f(1)+f(2)+......+f([a])} (C) [a]f(a)-{f(1)+f(2)+.......+fA} (D) af([a])-{f(1)+f(2)+......+fA}

If f(x)=[x], where [x] is the greatest integer function then find f(√2) ,f(3),f(-1.3),f(0),f(-1).

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^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

Given f^(prime)(1)=1"and"d/(dx)(f(2x))=f^(prime)(x)AAx > 0 .If f^(prime)(x) is differentiable then there exies a number c in (2,4) such that f''(c) equals