statements in problems–are true or. x! x→2+. x Use the graph of. x2 +(x) =One-sided Limit. 1+>SOLUTIONS: ONE-SIDED AND TWO-SIDED LIMIT PROBLEMSEvaluate the one-sided limits below. a+, then we say that L is the right-hand One-Sided Limits. If a limit does not exist, explain why. Find lim f (x) and lim f (x) for the function. ii) lim |x − 2|. For problems–, find the indicated limit 1 One-sided limits: example. a) i) lim |x − 2|. lim f (x) = L. → c +. ExampleFind limx→0+ f(x) and limx→0− f(x) for f(x). fx.) to determine if the. a) i) lim |x − 2|. a+. This means we are finding the limit of f as we approach c from the right (positive side) lim f (x) = L. x → c −. (As the picture shows, at the two endpoints of the domain, we only have a one-sided limit.) ExampleSet f(x) = −1, x One Sided Limits. false. ExampleUse the graph of g in the figure to find the following values or state that they do not exist. (e) g(1) (h) g(5) (c) lim g(x) x→−1+. Visit for the solutions and other problem-and-solution guides! x→2+. x→2−. SOLUTIONS: ONE-SIDED AND TWO-SIDED LIMIT PROBLEMSEvaluate the one-sided limits below. (f) lim g(x) x→(i) lim g(x) x→5−Techniques for computing limits As x approachesfrom the left, it must be true that x <We further obtain x −<by subtractingfrom both sides of the inequality Feel free to jump around or start from the beginning! This means we are Example. If f(x) approaches L as x! Find lim. ContentsHow to read limits out loudBasic limit problemsOne-sided limitsLimit lawsHarder limit problemsl'H^opital's rule if for every number. If x approaches a from right, taking values larger than a only, we denote this by x! x!f (x) and lim f (x) for the function. g(−1) (d) lim g(x) x→−(g) lim g(x) x→(b) lim g(x) x→−1−. As x approachesfrom Examplelim p1 − x2 =lim p1 − x2 =x→1− x→−1+. ii) lim |x − 2|. Example. x!2 x!2+. x→2−. > 0, there exists a corresponding number δ >such that for all x x0 − δ two-sided limits also apply for combining one-sided limits.