Let `g(x)=e^(f(x))a n df(x+1)=x+f(x)AAx in Rdot` If `n in I^+,t h e n(g^(prime)(n+1/2))/(g(n+1/2))-(g^(prime)(1/2))/(g(1/2))=` `2(1+1/2+1/3++1/n)` `2(1+1/3+1/5+1/(2n-1))` `n` 1

An inequation of the form f^((1)/(2)n)(x)

Let g^(prime)(x)>0a n df^(prime)(x)<0AAx in Rdot Then (f(x+1))>g(f(x-1)) f(g(x-1))>f(g(x+1)) g(f(x+1))

An inequation of the form f^((1)/(2)n)(x)

if f(x)=x^(n) then the value of f(1)-(f'(1))/(1!)+(f''(1))/(2!)+--+((-1)^(n)f^(prime--n)xx(1))/(n!)

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)(1)=2 b. G^(prime)(1)=3 c. G^(1)=2 d. G^(1)=3

Let g(x)=ln f(x) where f(x) is a twice differentiable positive function on (0,oo) such that f(x+1)=xf(x). Then for N=1,2,3g'(N+(1)/(2))-g'((1)/(2))=

If f(x)=x^(n),"n" epsilon N , then the value of f(1)-(f^(')(1))/(1!)+(f^(")(1))/(2!)-(f^''')(1)/(3!)+…+(-1)^(n)(f^(n)(1))/(n!) is

f(x)=(x^(n)-1)/(x-1),x!=1 and f(x)=n^(2),x=1 continuous at x=1 then the value of n