what does it means by 'positive lower bound'?

Answer 1

The largest positive number that is less than or equal to the (usually a function) value being referenced. As in, "The positive lower bound of 3sin(x) + 5 is 2." Or "The positive lower bound of
3 + 1/x is 3."

Doug

Answer 2

a bound is a value that a function cannot pass. The function f(x) = 1/x has a lower bound of 0 since no matter how big you make the values of x you will never get a value that is less than 0. The function f(x) = x^2 +1 has a lower bound of 1 since no matter how small you take x to be, the function will always be greater than or equal to 1. An example of an upper bound would be f(x) = -(x)^2. The value is bounded above by 0. So a positive lower bound is just a lower bound that is a positive number, like f(x) = x^2 +1 has a positive lower bound of 1.