New Tab Course material - MFE 1 - Sec 1 X 4HW - Google Drive X G poison ivy costume - Google S X C drive.google.com/drive/folders/1vXje9UWOhWJn63V2R3wCirexQhWVOPGW A Each of the following statements is false. Explain why, and then give a counterexample PDF using formulas or graphs. For example, the following statement is false: if lim f(x) = e, then lim f(x) = e. Indeed, a function can have different limits to the left and to the right. For instance, consider the function f (x) = 2x x+1 x>0. Then lim f(x) = 0, x-+0 but lim f(x) = 1, x-+0+ It would also be OK to draw the graph of such a function. 1. If lim f (x) = l, then f(a) = e. 2. If f is not continuous at a, then lim f (x) does not exist.New Tab Course material - MFE 1 - Sec 1 X 4HW - Google Drive X poison ivy costume - Google S( X C drive.google.com/drive/folders/1vXje9UWOhWJn63V2R3wCirexQhWVOPGW A : 2. If f is not continuous at a, then PDF lim f (x) cma does not exist. 3. If lim f (x) = e c-+a and lim g(x) = l, then f(a) = g(a). 4. If lim g(x) = 0, then lim f(x) x-a gx does not exist (it is not a real number). 5. If f(x) > 0 for all a E (-oo, too), then lim f(x) > 0. x-+0 3