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

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

If x gt 0 , show that, 1+x log (x+sqrt(x^(2)+1)) gt sqrt(1+x^(2))

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

Show that Lt_(x to 0)(log(1+x))/(x^(2))=1

Show that : Lt_(x to 0)(sqrt(1+x)-sqrt(1+x^(2)))/(sqrt(1+x^(2))-sqrt(1-x))=1

If f is a real function such that f(x)>0,f^(prime)(xx) is continuous for all real xa n da xf^(prime)(x)geq2sqrt(f(x))-2af(x),(a x!=2), show that sqrt(f(x))geq(sqrt(f(1)))/x ,xgeq1.