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. Examine the given graph and evaluate the following
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- Sketch a graph with the following characteristics: f'(x)>0, -inf<x<-1, 1<x<3 f'(x)<0, -1<x<0, 0<x<1, x>3 f"(x)>0, 0<x<2, 4<x<inf f"(x)<0, -inf<x<0, 2<x<4 f'(-1)=f'(-1)=f'(3)=0 f"(2)=f"(4)=0 lim x approaches inf f(x)=0 lim x approaches 0^- f(x)=-infEvaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .10. Determine whether lim g(x) exists or does not exist in the following graphs. x →1
- What is a limit, and what does it mean to say: lim f(x)=1? x->7-1. Is it possible that f(2) = 5 but limx→2f(x) = 7? If so, what kind of function can satisfy this?Let ƒ(x) = (x^2 - 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 limxS -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,c 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 xS -3. c. Find limxS -3 ƒ(x) algebraically.