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)]

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)]

Use the graph of f to estimate each limit, or write und (meaning undefined) if no limit exists. Use inf for ∞.limx→1−f(x)= limx→1+f(x)= limx→1f(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)

Calculate the following limits:(a) limx→0sin(2x2 + x3)x ; (b) limx→0√x(sin(1/x) − cos(1/x)).

Let f:→R→(0,∞) be strictly increasing function such that limx→∞f(7x)f(x)=1. Then, the value of limx→∞[f(5x)f(x)−1] is equal to