3- 2 01 -8-7-1 T 2 -3- # Determine which one of the following rules for continuity is first violated at a = - 1. Of(a) is defined. lim f(x) exists. O lim zIG f(x) = f(a).
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- Draw a graph where limx→2f(x) exists but f(x) is discontinuous at x = 2. Name the type of discontinuitythat has this propertyLet ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limx--> -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,...... instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as x -->-3.suppose f(X)-> -250 and g(x)->0 with g(x)>0 as x->2. Determine lim->2 f(x)/g(x)
- 2. Sketch the graph of a function, f, that satisfies the following properties:•x = 2 is a vertical asymptote•limx→∞ f(x) = 3•f′(−5) = 0 and f′(0) = 0•f′′(−5) = 0•f′′(−2) is undefined•f′(x) < 0 on (−2,0)•f′(x) > 0 on (−∞,−5) ∪ (−2,−5) ∪ (0,2) ∪ (2,∞)•f′′(x) > 0 on (−5,−2) ∪ (−2,2)•f′′(x) < 0 on (−∞,−5) ∪ (2,∞)Sketch a graph of a continuous curve with the following properties:f(1) =2 f(0) = 4 limX→±∞ f(X)=5f'(1)=f'(3) =0 f'(4) DNE F'(x) < 0 if − ∞ < x < 1 or 3 < x < 4F'(x)> 0 if 1 < x < 3 orx > 4F''(x)< 0 if − ∞< x < 0 or 2 <x< ∞f''(X) > 0 if 0 < x< 2Find the limit (if it exists) lim t2+t-2/t2-1 t-->1