Question

I missed an important class today due to being sick and I have a quiz tomorrow; can someone please explain one sided limits to me ?

Answer 1

With a one-sided limit, you test values really close to the value x is approaching, but from only one side. Say that you want to find the left-hand limit as x approaches zero of 1/x. You substitute values like -.001, because the limit is from the left. If you were looking for the right hand limit, you would test values from the right, like .001. The only reason this is done is to explain discontinuities and some derivatives in calculus\[\lim_{x \rightarrow 0}\frac{ 1 }{ x }\]does not exist because the limit from the left is not equal to the limit from the right. From the left (that is, with values of x coming from the left of 0 but never equaling it), the limit is negative infinity. From the right the limit is positive infinity.

Answer 2

but a question like \[\lim_{x \rightarrow 2^+} \sqrt{2-x}\]