Given that lim x→1 f(x) = 1    lim x→1 g(x) = −2    lim x→1 h(x) = 0,find each limit, if it exists. (If an answer does not exist, enter DNE.)(a)lim x→1 [f(x) + 3g(x)] (b)lim x→1 [g(x)]3 (c)lim x→1 f(x) (d)lim x→1 4f(x)g(x) (e)lim x→1 g(x)h(x) (f)lim x→1 g(x)h(x)f(x)

Use the graphs of f and g in the accompanying figure tofind the limits that exist. If the limit does not exist, explainwhy.(a) limx → 2 [f(x) + g(x)]

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true?I. g(x) = 1 at least onceII. lim⁡𝑥→3.5𝑔(𝑥)=𝑔(3.5)III. lim⁡𝑥→3−𝑔(𝑥)=lim⁡𝑥→3+𝑔(𝑥)​ I. g(x) = 1 at least onceII.  x→3.5lim​ g(x)=g(3.5)III.  x→3−lim​ g(x)= x→3+lim​ g(x)​

Define f, g : R → R by f (x) = (x − 2)2 andg(x) =1 if x > 0,0 if x = 0,−1 if x < 0.Calculatelimx→2 g(f (x)) and g limx→2 f (x)

Decide whether the limit exists. If it exists, find its value.lim f(x)x→1

(a) limx→1x2 − 1x − 1