dicuss the behaviour of y=(x=4)/(2x+1) as x->infinity
To discuss the behavior of the function y=(x+4)/(2x+1) as x approaches infinity, we can look at the limit of the function as x grows without bound.
Taking the limit as x approaches infinity, we have:
lim (x→∞) (x+4)/(2x+1)
To find this limit, we can divide every term in the numerator and denominator by the highest power of x, which is x in this case:
lim (x→∞) (1+4/x)/(2+1/x)
As x approaches infinity, the terms 4/x and 1/x become arbitrarily close to zero, so we can disregard them:
lim (x→∞) (1+0)/(2+0) = 1/2
Therefore, as x approaches infinity, the behavior of the function y=(x+4)/(2x+1) is such that y approaches 1/2. This means that as x gets larger and larger, the function values get closer and closer to 1/2.