The minimum value of `x/((log)_e x)` is `e` (b) `1//e` (c) 1 (d) none of these

The minimum value of x\ (log)_e x is equal to e (b) 1//e (c) -1//e (d) 2e (e) e

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0

The maximum value of x^(1/x),x >0 is (a) e^(1/e) (b) (1/e)^e (c) 1 (d) none of these

The maximum value of x^(1/x),x >0 is (a) e^(1/e) (b) (1/e)^e (c) 1 (d) none of these

The maximum value of (logx)/x is (a) 1 (b) 2/e (c) e (d) 1/e

The differential coefficient of f((log)_e x) with respect to x , where f(x)=(log)_e x , is (a) x/((log)_e x) (b) 1/x(log)_e x (c) 1/(x(log)_e x) (d) none of these

The value of lim_(m->oo)(cos(x/m))^("m") is 1 (b) e (c) e^(-1) (d) none of these

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to (a) 0 (b) 1/e (c) e (d) none of these

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_e 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these