If `("lim")_(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2,` then find the value of `f^(prime)(0)dot` a) 4 (b) 2 (c) 0 (d) 1

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

If f(0)=1,f(2)=3,f^'(2)=5 ,then find the value of int_0^1xf^('')(2x)dx

f(x)=int_1^x(tan^(-1)(t))/t dt , x in R^+, then find the value of f(e^2)-f(1/(e^2))

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

If int_(0)^(x) f ( t) dt = x + int_(x)^(1) tf (t) dt , then the value of f(1) is

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)=lim_(n->oo)((x^2+a x+1)+x^(2n)(2x^2+x+b))/(1+x^(2n))and lim_(x->+-1)f(x) exist, then The value of b is (a) -1 (b). 1 ( c.) 0 (d). 2

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx