Area bounded by `y = ln(x + )1, y =lnx + 1` and their common tangent is (A) `1-ln(e-1)` (B) `1+ln(e-1)` (C) `1/2+ln(e-1)` (D) `-1/2+ln(e-1)`

The area of bounded by e^(ln(x+1)) ge |y|, |x| le 1 is….

The area of bounded by e^(ln(x+1)) ge |y|, |x| le 1 is….

"If "f: [-1,1]rarr[-(1)/(2),(1)/(2)]:f(x)=(x)/(1+x^(2)), then find the area bounded by y=f^(-1)(x), the x -axis and the lines x=(1)/(2), x=-(1)/(2). a. 1/2 log e " " b. log(e/2) c. 1/2 log e/3 " " d. 1/2 log (e/2)

The area of the region bonded by y=e^(x),y=e^(-x),x=0 and x = 1 is (a) e+(1)/(e) (b) log(4/e) (c) 4log(4/e) (d) e+(1)/(e)-2

underset(e^(x)-1)^(2)(e^(x)-1)^(2)dx+A log(e^(x)-1)+(B)/(e^(x)-1)

The curve x = log y+ e and y = log (1/x)

(1) / (log_ (3) e) + (1) / (log_ (3) e ^ (2)) + (1) / (log_ (3) e ^ (4)) + ... =

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

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

lim _( x to 0) [ (2 ^(x) -1)/( sqrt (1 + ) x-1 )] is equal to: a) log _(e) 2 b) log _(e) sqrt2 c) log _(e) 4 d) 1/2