ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)...

`ifint(dx)/(x^2(x^n+1)^(((n-1)/n))=-[f(x)]^(1/n)+c ,t h e nf(x)i s` `(1+x^n)` (b) `1+x^(-1)` `x^n+x^(-n)` (d) none of these

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ifint(dx)/(x^2(x^n+1)^(((n-1)/n)) )=-[f(x)]^(1/n)+c ,t h e nf(x)i s (a) (1+x^n) (b) 1+x^(-1) (c) x^n+x^(-n) (d) none of these

If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (A) 1+x^n (B) 1+x^-n (C) x^n+x^-n (D) x^n-x^-n

int dx/(x^n(1+x^n)^(1/n)) is

If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2),t h e n(dy)/(dx) at x=1 is (a)2 (b) 1 (c) -2 (d) none of these

lim_(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x (c) (log)_e x (d) none of these

If intsin^(-1)xcos^(-1)xdx=f^(-1)(x)[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n (a) f(x)=sinx (b) f(x)=cosx (c) f(x)=tanx (d) none of these

(d^n)/(dx^n)(logx)=? (a) ((n-1)!)/(x^n) (b) (n !)/(x^n) (c) ((n-2)!)/(x^n) (d) (-1)^(n-1)((n-1)!)/(x^n)

f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim_(x->oo)f(x) is equal to (a) 1 (b) 1/2 (c) 2 (d) none of these

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (a) (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) (c) 1/(2xsqrt(x^2-1)) (d) none of these

Ifint_(log2)^x(dx)/(sqrt(e^x-1))=pi/6,"then " x " is equalto" 4 (b) 1n 8 (c) 1n 4 (d) none of these

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