lim(sqrt(x^4-x^2))=0
True or false?
if you have limit as x->2, then TRUE
i have limit x->0
Oh, my bad. I read it as sqrt(4-x^2)
If x->0, then since x^4 and x^2 are both 0, then limit is also 0, so TRUE.
so, right answer, wrong reason. :-)
To determine whether the statement lim(sqrt(x^4-x^2))=0 is true or false, we need to evaluate the limit of the given function as x approaches a particular value or infinity.
To evaluate this limit, we can simplify the expression inside the square root:
sqrt(x^4 - x^2) = sqrt(x^2(x^2 - 1)) = sqrt(x^2) * sqrt(x^2 - 1) = x * sqrt(x^2 - 1)
Now, we can see that as x approaches infinity, the expression x^2 - 1 becomes larger and larger. As a result, sqrt(x^2 - 1) also grows without bound. Therefore, the limit of x * sqrt(x^2 - 1) as x approaches infinity is infinity, not 0.
Hence, the statement lim(sqrt(x^4-x^2))=0 is false.