Let `f(x)` be the fourth degree polynomial such that `f^(prime)(0)-6,f(0)=2a n d(lim)_(xvec1)(f(x))/((x-1)^2)=1` The value of `f(2)` is `3` b. 1 c. `0` d.`2`

Let f(x) be the fourth degree polynomial such that f^(prime)(0)=-6,f(0)=2 and (lim)_(x->1)(f(x))/((x-1)^2)=1 The value of f(2) is a. 3 b. 1 c. 0 d. 2

Let f(x) be the fourth degree polynomial such that f'(0)-6,f(0)=2 and lim_(x rarr1)(f(x))/((x-1)^(2))=1 The value of f(2) is 3 b.1 c.0 d.2

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

Let ("lim")_(xvec1)(x^a-a x+a-1)/((x-1)^2)=f(a)dot Then the value of f(4) is _________

Let f(x) be a function such that ("lim")_(xvec0)(f(x))/x=1 and ("lim")_(xvec0)(x(1+acosx)-bsinx)/((f(x))^3)=1 , then b-3a is equal to

If f(x) is a polynomial of degree 2, such that f(0)=3,f'(0)=-7,f''(0)=8 int_(1)^(2)f(x)dx=

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

Let f(x) be differentiable for real x such that f^(prime)(x)>0on(-oo,-4), f^(prime)(x) 0on(6,oo), If g(x)=f(10-2x), then the value of g^(prime)(2) is a. 1 b. 2 c. 0 d. 4

If f(x) is a polynomial of degree n such that f(0)=0,f(x)=(1)/(2),...,f(n)=(n)/(n+1) then the value of f(n+1) is

Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,f^('')(3)=0,a n df^(''')(3)=12. Then the value of f^(prime)(1) is (a) 12 (b) 23 (c) -13 (d) none of these