Show that `1+xin(x+sqrt(x^2+1))geqsqrt(1+x^2)` for all `xgeq0.`

Show that 1+x ln(x+sqrt(x^(2)+1))>=sqrt(1+x^(2)) for all x>=0

Show that log(x+sqrt(1+x^(2))) 1

Show that 1 + x log (x + sqrt (x ^(2) + 1)) ge sqrt ( 1 + x ^(2)) AA x ge 0

Show that lim_(x rarr0)(e^(x)-1)/(sqrt(1+x)-1)=2

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

Show that x(sqrt(x)-sqrt(x+1)) is not differentiable at x=0

If f(x)=sqrt(1-sqrt(1-x^(2))) then at x=0

Show that f(x) = (1)/((1 + x^(2))) is increasing for all x le 0

(1) x^(2)-(sqrt(2)+1)x+sqrt(2)=0

If a,b are real and a^(2)+b^(2)=1, then show that the equation (sqrt(1+x)-i sqrt(1-x))/(sqrt(1+x)+i sqrt(1-x))=a-ib is satisfied y a real value of x.