Question

2 *3 X3 6. Consider a function y = f(x) such that lim f(x) = 2, lim f(x) = 2, and f(3) = -1. Explain whether each statement is true or false. a) y=f(x) is continuous at x = 3. b) The limit of f(x) as x approaches 3 does not exist. c) The value of the left-hand limit is 2. d) The value of the right-hand limit is -1. e) When x = 3, the y-value of the function is 2.

Answer 1

x approaches 3 derrot We know at (n=al Herce, y = f(x). limit of y=f(x) exists lim, fox) exists if limfox) una naye+ at Mama Again we know f(n) is continuom , I lim fex) lim fex) = fra na Na at <aj Given that lim f(x) = 2 lim f(x) = 2 x 5 23t and f(3) = -1 Here slim f1x) = 2 -lim tony = f(3) = -1 se x + 3 R-739 so, froy مد not continuous at a=3 bo,) ii False (6) lim f(x) = lim f(x) = 2, X-3* Here, lim x 3 bo, limit of tox as exist. is False 1 (1)

since lim f(x) =2 x 73 The value of the left-hamed limit is 2 So <c) is ture d Since lim tex) = 2 +-1 x=3+ 30, the value of the right hand limit is a not -1 Fabe (d) is ren the ya value ie f(3) =-1. At a = 3, so, ya value of the function in (-2) 30 option @ is Fabe