Question

3. Given that lim f(x) = 4 and lim f(x) = -4, what is true about lim f(x)? x-1 4. Given that lim f(x) = 1, lim f(x) = 1, and f(-3) = 1, what is true about lim f(x)? 5. Given that lim f(x) = 0, lim f(x) = 0, and f(2) = 3, what is true about limf(x)? X-3 X-3 X-2

Answer 1

limfn) and Nyat Nya exist and also it at raa & Condition of timi existance of limit of a Function : of lim fong exists and lim fm) lim fox) = limfm) then can be said that of limit of f exist point a. denote it as lim fx) Again if fcas has a finite value and limfax) = fcas then we that Bay is continuous at the point a. at the point a. and we nga 에 xta Mans Here lim fcas = 4 xyl xit Thus we nyi see that lim fm) - lim fra). is limfne) does not exist. 1 A. Given that lim of (x) = 1, lim fox) = 1, lim fra)=1 Ny-3t H4-3- This we that lim f(x) see lim f(x) = lim fime) = 1 xy-3 xy-3+ & limf (e) = xy-3 Also it is given that f(3) = 1 Hence Lim from y = 1 = f(-3). Therefore that f is continuous we say can say at the point (-) . 27-3

lloy lim fox) = 0 22 lim f(x) = 0 naat Thus we see that lim fex) = lim of (x). Mayat we conclude that limfres exist and it equal to n 2- so x2 0. lim f (x)=0 ny2 x 2 But here it is given that f (2) = 3. Hence we see that lim f(x) = 073 = f(2) le lim fon) & f (2) Therefore f is not continuous at the point x2 x = 2. O
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