Math 111H Problem Set 1, Fall 2012Read each problem carefully. Show all your work for each problem! Use only those methods discussedthus far in class.1. Givenf(x)=x2+4,Fnd the average rate of change on the interval [-1, 3]. ±ind a point on thisinterval where the instantaneous rate of change is equal to the average rate of change just found.2. Evaluate the following limitlimx→2√6−x−2√3−x−1.3. ±ind all values of the constant,a,so thatf(3) = limx→3f(x).f(x°x2−9x−3+a,x°=3a2,x.4. ±or the given function, (i) sketch by handf(x) on the intervalx∈[−2,2],and (ii) evaluate thelimits limx→0f(x) and limx→1f(x),if they exist.f(x|x+1|≤0x|x|+x,0<x≤13−x,x >1.5. Use MATLAB to plot the functions sin
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