Answer to Question #217736 in Calculus for livy

Question

State, with explanation, whether the following statements are True or False: a) If a real-valued function is defined on (−∞, 𝑐) ∪ (𝑐, ∞) and has a removable discontinuity at 𝑥 = 𝑐, then lim𝑥→𝑐 𝑓(𝑥) does not exist. b) Since 𝑓(𝑥) = 1 𝑥−1 + 1 has a vertical asymptote at 𝑥 = 1, the Intermediate Value Theorem cannot be used to find an existence of a root in the open interval (−1, 1 2 ).