Consider the function below. lim x -> 3 (2x+1)=7 What values of x guarantee that f(x)=2x+1 is within 0.54 units of 7? If x is within _____ units of 3, then f(x) is within 0.54 units of 7.

Question

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Answer 1

f(x+h)=V+k where x=3 and V=7. h is the “within” value for x and k is the “within” value of V.

So f(x+h)=2(x+h)+1=2x+2h+q=V+k. (We could also write f(x-h)=V-k, etc.)

So we put x=3, V=7 and k=0.54: 6+2h+1=7+0.54; 7+2h=7+0.54, 2h=0.54, h=0.27.

Therefore, if x is within 0.27 units of 3, then f(x) is within 0.54 units of 7.