How do you evaluate the limit from either direction of one-sided limits?

The limit at c doesnt exist because the limit from the left is different than from the right. How do you evaluate the limits at c from the left and from the right separately?|||I liked this question. I too would like to know. No one has yet to answer, really. People are saying "use intuition"... I dont know about any algebraic methods.





You know what I wonder about? What is the limit as x approaches 0 of the square root of x


lim_{x鈫?} 鈭歺





Seems simple, right? In fact, you can evaluate a specific value at x=0. The 鈭? = 0. The function has a value and it exists at x=0.





But... and here is the kicker... the limit only exists from the right. You cannot evaluate the limit from the left. And, therefore, by definition, the limit itself doesnt exist.





The function has a value at a given x-value, the right hand limit evaluates to the same... but the left hand and generic limits dont exist.





Tell me how that is intuitive?|||It depends on the function you're studying.





For example, lim(x-%26gt;0) 1/(e^(1/x)+1) does not exist.





If x -%26gt;0+, 1/x is greater and greater, but always positive, and then e^(1/x) goes to infinity. Then this lateral limit is zero.





But if x-%26gt;0-, 1/x is more and more negative (goes to -infinity), and then e^(1/x) goes to zero. This lateral limit is 1.





You must examine the function carefully, looking for asymmetries like this.|||the way you evaluate is as the limit aprroaches C from the right you ask yourself what happens what number does it get close to same as it approaches C from the left , it also depends on the function that you are taking the limit of,